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geometry</title> <meta name="description" content="Search results for: stochastic geometry"> <meta name="keywords" content="stochastic geometry"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="stochastic geometry"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 1567</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: stochastic geometry</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1567</span> On Virtual Coordination Protocol towards 5G Interference Mitigation: Modelling and Performance Analysis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bohli%20Afef">Bohli Afef</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The fifth-generation (5G) wireless systems is featured by extreme densities of cell stations to overcome the higher future demand. Hence, interference management is a crucial challenge in 5G ultra-dense cellular networks. In contrast to the classical inter-cell interference coordination approach, which is no longer fit for the high density of cell-tiers, this paper proposes a novel virtual coordination based on the dynamic common cognitive monitor channel protocol to deal with the inter-cell interference issue. A tractable and flexible model for the coverage probability of a typical user is developed through the use of the stochastic geometry model. The analyses of the performance of the suggested protocol are illustrated both analytically and numerically in terms of coverage probability. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=ultra%20dense%20heterogeneous%20networks" title="ultra dense heterogeneous networks">ultra dense heterogeneous networks</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20common%20channel%20protocol" title=" dynamic common channel protocol"> dynamic common channel protocol</a>, <a href="https://publications.waset.org/abstracts/search?q=cognitive%20radio" title=" cognitive radio"> cognitive radio</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20geometry" title=" stochastic geometry"> stochastic geometry</a>, <a href="https://publications.waset.org/abstracts/search?q=coverage%20probability" title=" coverage probability"> coverage probability</a> </p> <a href="https://publications.waset.org/abstracts/69891/on-virtual-coordination-protocol-towards-5g-interference-mitigation-modelling-and-performance-analysis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/69891.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">325</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1566</span> Stochastic Age-Structured Population Models</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov">Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson鈥檚 blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boundary%20value%20problems" title="boundary value problems">boundary value problems</a>, <a href="https://publications.waset.org/abstracts/search?q=population%20models" title=" population models"> population models</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20delay%20differential%20equations" title=" stochastic delay differential equations"> stochastic delay differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20partial%20differential%20equation" title=" stochastic partial differential equation"> stochastic partial differential equation</a> </p> <a href="https://publications.waset.org/abstracts/138398/stochastic-age-structured-population-models" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/138398.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">254</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1565</span> Performance Analysis of Heterogeneous Cellular Networks with Multiple Connectivity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sungkyung%20Kim">Sungkyung Kim</a>, <a href="https://publications.waset.org/abstracts/search?q=Jee-Hyeon%20Na"> Jee-Hyeon Na</a>, <a href="https://publications.waset.org/abstracts/search?q=Dong-Seung%20Kwon"> Dong-Seung Kwon</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Future mobile networks following 5th generation will be characterized by one thousand times higher gains in capacity; connections for at least one hundred billion devices; user experience capable of extremely low latency and response times. To be close to the capacity requirements and higher reliability, advanced technologies have been studied, such as multiple connectivity, small cell enhancement, heterogeneous networking, and advanced interference and mobility management. This paper is focused on the multiple connectivity in heterogeneous cellular networks. We investigate the performance of coverage and user throughput in several deployment scenarios. Using the stochastic geometry approach, the SINR distributions and the coverage probabilities are derived in case of dual connection. Also, to compare the user throughput enhancement among the deployment scenarios, we calculate the spectral efficiency and discuss our results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=heterogeneous%20networks" title="heterogeneous networks">heterogeneous networks</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20connectivity" title=" multiple connectivity"> multiple connectivity</a>, <a href="https://publications.waset.org/abstracts/search?q=small%20cell%20enhancement" title=" small cell enhancement"> small cell enhancement</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20geometry" title=" stochastic geometry"> stochastic geometry</a> </p> <a href="https://publications.waset.org/abstracts/25414/performance-analysis-of-heterogeneous-cellular-networks-with-multiple-connectivity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25414.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">331</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1564</span> Non-Stationary Stochastic Optimization of an Oscillating Water Column</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mar%C3%ADa%20L.%20Jal%C3%B3n">Mar铆a L. Jal贸n</a>, <a href="https://publications.waset.org/abstracts/search?q=Feargal%20Brennan"> Feargal Brennan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-stationary%20stochastic%20optimization" title="non-stationary stochastic optimization">non-stationary stochastic optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=oscillating%20water" title=" oscillating water"> oscillating water</a>, <a href="https://publications.waset.org/abstracts/search?q=temporal%20variability" title=" temporal variability"> temporal variability</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20energy" title=" wave energy"> wave energy</a> </p> <a href="https://publications.waset.org/abstracts/75300/non-stationary-stochastic-optimization-of-an-oscillating-water-column" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/75300.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">373</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1563</span> Weak Solutions Of Stochastic Fractional Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lev%20Idels">Lev Idels</a>, <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov"> Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=delay%20equations" title="delay equations">delay equations</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20methods" title=" operator methods"> operator methods</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20noise" title=" stochastic noise"> stochastic noise</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20solutions" title=" weak solutions"> weak solutions</a> </p> <a href="https://publications.waset.org/abstracts/146592/weak-solutions-of-stochastic-fractional-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/146592.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">209</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1562</span> Lyapunov and Input-to-State Stability of Stochastic Differential Equations </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov">Arcady Ponosov</a>, <a href="https://publications.waset.org/abstracts/search?q=Ramazan%20Kadiev"> Ramazan Kadiev</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Input-to-State Stability (ISS) is widely used in deterministic control theory but less known in the stochastic case. Roughly speaking, the theory explains when small perturbations of the right-hand sides of the system on the entire semiaxis cause only small changes in the solutions of the system, again on the entire semiaxis. This property is crucial in many applications. In the report, we explain how to define and study ISS for systems of linear stochastic differential equations with or without delays. The central result connects ISS with the property of Lyapunov stability. This relationship is well-known in the deterministic setting, but its stochastic version is new. As an application, a method of studying asymptotic Lyapunov stability for stochastic delay equations is described and justified. Several examples are provided that confirm the efficiency and simplicity of the framework. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20stability" title="asymptotic stability">asymptotic stability</a>, <a href="https://publications.waset.org/abstracts/search?q=delay%20equations" title=" delay equations"> delay equations</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20methods" title=" operator methods"> operator methods</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20perturbations" title=" stochastic perturbations"> stochastic perturbations</a> </p> <a href="https://publications.waset.org/abstracts/127764/lyapunov-and-input-to-state-stability-of-stochastic-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127764.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">175</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1561</span> Stochastic Energy and Reserve Scheduling with Wind Generation and Generic Energy Storage Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Amirhossein%20Khazali">Amirhossein Khazali</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohsen%20Kalantar"> Mohsen Kalantar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Energy storage units can play an important role to provide an economic and secure operation of future energy systems. In this paper, a stochastic energy and reserve market clearing scheme is presented considering storage energy units. The approach is proposed to deal with stochastic and non-dispatchable renewable sources with a high level of penetration in the energy system. A two stage stochastic programming scheme is formulated where in the first stage the energy market is cleared according to the forecasted amount of wind generation and demands and in the second stage the real time market is solved according to the assumed scenarios. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=energy%20and%20reserve%20market" title="energy and reserve market">energy and reserve market</a>, <a href="https://publications.waset.org/abstracts/search?q=energy%20storage%20device" title=" energy storage device"> energy storage device</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20programming" title=" stochastic programming"> stochastic programming</a>, <a href="https://publications.waset.org/abstracts/search?q=wind%20generation" title=" wind generation"> wind generation</a> </p> <a href="https://publications.waset.org/abstracts/36215/stochastic-energy-and-reserve-scheduling-with-wind-generation-and-generic-energy-storage-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36215.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">574</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1560</span> Sufficient Conditions for Exponential Stability of Stochastic Differential Equations with Non Trivial Solutions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fakhreddin%20Abedi">Fakhreddin Abedi</a>, <a href="https://publications.waset.org/abstracts/search?q=Wah%20June%20Leong"> Wah June Leong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=exponential%20stability%20in%20probability" title="exponential stability in probability">exponential stability in probability</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20differential%20equations" title=" stochastic differential equations"> stochastic differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov%20technique" title=" Lyapunov technique"> Lyapunov technique</a>, <a href="https://publications.waset.org/abstracts/search?q=Ito%27s%20formula" title=" Ito's formula"> Ito's formula</a> </p> <a href="https://publications.waset.org/abstracts/184321/sufficient-conditions-for-exponential-stability-of-stochastic-differential-equations-with-non-trivial-solutions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/184321.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">52</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1559</span> Finding DEA Targets Using Multi-Objective Programming</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Farzad%20Sharifi">Farzad Sharifi</a>, <a href="https://publications.waset.org/abstracts/search?q=Raziyeh%20Shamsi"> Raziyeh Shamsi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we obtain the projection of inefficient units in data envelopment analysis (DEA) in the case of stochastic inputs and outputs using the multi-objective programming (MOP) structure. In some problems, the inputs might be stochastic while the outputs are deterministic, and vice versa. In such cases, we propose molti-objective DEA-R model, because in some cases (e.g., when unnecessary and irrational weights by the BCC model reduces the efficiency score), an efficient DMU is introduced as inefficient by the BCC model, whereas the DMU is considered efficient by the DEA-R model. In some other case, only the ratio of stochastic data may be available (e.g; the ratio of stochastic inputs to stochastic outputs). Thus, we provide multi objective DEA model without explicit outputs and prove that in-put oriented MOP DEA-R model in the invariable return to scale case can be replacing by MOP- DEA model without explicit outputs in the variable return to scale and vice versa. Using the interactive methods for solving the proposed model, yields a projection corresponding to the viewpoint of the DM and the analyst, which is nearer to reality and more practical. Finally, an application is provided. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=DEA" title="DEA">DEA</a>, <a href="https://publications.waset.org/abstracts/search?q=MOLP" title=" MOLP"> MOLP</a>, <a href="https://publications.waset.org/abstracts/search?q=STOCHASTIC" title=" STOCHASTIC"> STOCHASTIC</a>, <a href="https://publications.waset.org/abstracts/search?q=DEA-R" title=" DEA-R"> DEA-R</a> </p> <a href="https://publications.waset.org/abstracts/59723/finding-dea-targets-using-multi-objective-programming" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59723.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">398</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1558</span> Finding Data Envelopment Analysis Targets Using Multi-Objective Programming in DEA-R with Stochastic Data</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=R.%20Shamsi">R. Shamsi</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Sharifi"> F. Sharifi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we obtain the projection of inefficient units in data envelopment analysis (DEA) in the case of stochastic inputs and outputs using the multi-objective programming (MOP) structure. In some problems, the inputs might be stochastic while the outputs are deterministic, and vice versa. In such cases, we propose a multi-objective DEA-R model because in some cases (e.g., when unnecessary and irrational weights by the BCC model reduce the efficiency score), an efficient decision-making unit (DMU) is introduced as inefficient by the BCC model, whereas the DMU is considered efficient by the DEA-R model. In some other cases, only the ratio of stochastic data may be available (e.g., the ratio of stochastic inputs to stochastic outputs). Thus, we provide a multi-objective DEA model without explicit outputs and prove that the input-oriented MOP DEA-R model in the invariable return to scale case can be replaced by the MOP-DEA model without explicit outputs in the variable return to scale and vice versa. Using the interactive methods for solving the proposed model yields a projection corresponding to the viewpoint of the DM and the analyst, which is nearer to reality and more practical. Finally, an application is provided. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=DEA-R" title="DEA-R">DEA-R</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-objective%20programming" title=" multi-objective programming"> multi-objective programming</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20data" title=" stochastic data"> stochastic data</a>, <a href="https://publications.waset.org/abstracts/search?q=data%20envelopment%20analysis" title=" data envelopment analysis"> data envelopment analysis</a> </p> <a href="https://publications.waset.org/abstracts/154613/finding-data-envelopment-analysis-targets-using-multi-objective-programming-in-dea-r-with-stochastic-data" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/154613.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">105</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1557</span> Interactive Winding Geometry Design of Power Transformers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Paffrath%20Meinhard">Paffrath Meinhard</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhou%20Yayun"> Zhou Yayun</a>, <a href="https://publications.waset.org/abstracts/search?q=Guo%20Yiqing"> Guo Yiqing</a>, <a href="https://publications.waset.org/abstracts/search?q=Ertl%20Harald"> Ertl Harald</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Winding geometry design is an important part of power transformer electrical design. Conventionally, the winding geometry is designed manually, which is a time-consuming job because it involves many iteration steps in order to meet all cost, manufacturing and electrical requirements. Here a method is presented which automatically generates the winding geometry for given user parameters and allows the user to interactively set and change parameters. To achieve this goal, the winding problem is transferred to a mixed integer nonlinear optimization problem. The relevant geometrical design parameters are defined as optimization variables. The cost and other requirements are modeled as constraints. For the solution, a stochastic ant colony optimization algorithm is applied. It is well-known, that an optimizer can get stuck in a local minimum. For the winding problem, we present efficient strategies to come out of local minima, furthermore a reduced variable search range helps to accelerate the solution process. Numerical examples show that the optimization result is delivered within seconds such that the user can interactively change the variable search area and constraints to improve the design. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=ant%20colony%20optimization" title="ant colony optimization">ant colony optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed%20integer%20nonlinear%20programming" title=" mixed integer nonlinear programming"> mixed integer nonlinear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20transformer" title=" power transformer"> power transformer</a>, <a href="https://publications.waset.org/abstracts/search?q=winding%20design" title=" winding design"> winding design</a> </p> <a href="https://publications.waset.org/abstracts/74700/interactive-winding-geometry-design-of-power-transformers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/74700.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">380</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1556</span> A Multi-Objective Programming Model to Supplier Selection and Order Allocation Problem in Stochastic Environment</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rouhallah%20Bagheri">Rouhallah Bagheri</a>, <a href="https://publications.waset.org/abstracts/search?q=Morteza%20Mahmoudi"> Morteza Mahmoudi</a>, <a href="https://publications.waset.org/abstracts/search?q=Hadi%20Moheb-Alizadeh"> Hadi Moheb-Alizadeh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper aims at developing a multi-objective model for supplier selection and order allocation problem in stochastic environment, where purchasing cost, percentage of delivered items with delay and percentage of rejected items provided by each supplier are supposed to be stochastic parameters following any arbitrary probability distribution. In this regard, dependent chance programming is used which maximizes probability of the event that total purchasing cost, total delivered items with delay and total rejected items are less than or equal to pre-determined values given by decision maker. The abovementioned stochastic multi-objective programming problem is then transformed into a stochastic single objective programming problem using minimum deviation method. In the next step, the further problem is solved applying a genetic algorithm, which performs a simulation process in order to calculate the stochastic objective function as its fitness function. Finally, the impact of stochastic parameters on the given solution is examined via a sensitivity analysis exploiting coefficient of variation. The results show that whatever stochastic parameters have greater coefficients of variation, the value of the objective function in the stochastic single objective programming problem is deteriorated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=supplier%20selection" title="supplier selection">supplier selection</a>, <a href="https://publications.waset.org/abstracts/search?q=order%20allocation" title=" order allocation"> order allocation</a>, <a href="https://publications.waset.org/abstracts/search?q=dependent%20chance%20programming" title=" dependent chance programming"> dependent chance programming</a>, <a href="https://publications.waset.org/abstracts/search?q=genetic%20algorithm" title=" genetic algorithm"> genetic algorithm</a> </p> <a href="https://publications.waset.org/abstracts/32384/a-multi-objective-programming-model-to-supplier-selection-and-order-allocation-problem-in-stochastic-environment" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32384.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">313</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1555</span> Gamification Using Stochastic Processes: Engage Children to Have Healthy Habits </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Andre%20M.%20Carvalho">Andre M. Carvalho</a>, <a href="https://publications.waset.org/abstracts/search?q=Pedro%20Sebastiao"> Pedro Sebastiao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This article is based on a dissertation that intends to analyze and make a model, intelligently, algorithms based on stochastic processes of a gamification application applied to marketing. Gamification is used in our daily lives to engage us to perform certain actions in order to achieve goals and gain rewards. This strategy is an increasingly adopted way to encourage and retain customers through game elements. The application of gamification aims to encourage children between 6 and 10 years of age to have healthy habits and the purpose of serving as a model for use in marketing. This application was developed in unity; we implemented intelligent algorithms based on stochastic processes, web services to respond to all requests of the application, a back-office website to manage the application and the database. The behavioral analysis of the use of game elements and stochastic processes in children鈥檚 motivation was done. The application of algorithms based on stochastic processes in-game elements is very important to promote cooperation and to ensure fair and friendly competition between users which consequently stimulates the user鈥檚 interest and their involvement in the application and organization. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=engage" title="engage">engage</a>, <a href="https://publications.waset.org/abstracts/search?q=games" title=" games"> games</a>, <a href="https://publications.waset.org/abstracts/search?q=gamification" title=" gamification"> gamification</a>, <a href="https://publications.waset.org/abstracts/search?q=randomness" title=" randomness"> randomness</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20processes" title=" stochastic processes"> stochastic processes</a> </p> <a href="https://publications.waset.org/abstracts/85625/gamification-using-stochastic-processes-engage-children-to-have-healthy-habits" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/85625.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">329</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1554</span> Supplier Selection and Order Allocation Using a Stochastic Multi-Objective Programming Model and Genetic Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rouhallah%20Bagheri">Rouhallah Bagheri</a>, <a href="https://publications.waset.org/abstracts/search?q=Morteza%20Mahmoudi"> Morteza Mahmoudi</a>, <a href="https://publications.waset.org/abstracts/search?q=Hadi%20Moheb-Alizadeh"> Hadi Moheb-Alizadeh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we develop a supplier selection and order allocation multi-objective model in stochastic environment in which purchasing cost, percentage of delivered items with delay and percentage of rejected items provided by each supplier are supposed to be stochastic parameters following any arbitrary probability distribution. To do so, we use dependent chance programming (DCP) that maximizes probability of the event that total purchasing cost, total delivered items with delay and total rejected items are less than or equal to pre-determined values given by decision maker. After transforming the above mentioned stochastic multi-objective programming problem into a stochastic single objective problem using minimum deviation method, we apply a genetic algorithm to get the later single objective problem solved. The employed genetic algorithm performs a simulation process in order to calculate the stochastic objective function as its fitness function. At the end, we explore the impact of stochastic parameters on the given solution via a sensitivity analysis exploiting coefficient of variation. The results show that as stochastic parameters have greater coefficients of variation, the value of objective function in the stochastic single objective programming problem is worsened. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dependent%20chance%20programming" title="dependent chance programming">dependent chance programming</a>, <a href="https://publications.waset.org/abstracts/search?q=genetic%20algorithm" title=" genetic algorithm"> genetic algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=minimum%20deviation%20method" title=" minimum deviation method"> minimum deviation method</a>, <a href="https://publications.waset.org/abstracts/search?q=order%20allocation" title=" order allocation"> order allocation</a>, <a href="https://publications.waset.org/abstracts/search?q=supplier%20selection" title=" supplier selection"> supplier selection</a> </p> <a href="https://publications.waset.org/abstracts/42319/supplier-selection-and-order-allocation-using-a-stochastic-multi-objective-programming-model-and-genetic-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42319.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">256</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1553</span> Stochastic Variation of the Hubble's Parameter Using Ornstein-Uhlenbeck Process</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mary%20Chriselda%20A">Mary Chriselda A</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble鈥檚 Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chapman%20Kolmogorov%20forward%20differential%20equations" title="Chapman Kolmogorov forward differential equations">Chapman Kolmogorov forward differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=fourier%20transformation" title=" fourier transformation"> fourier transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=hubble%27s%20parameter" title=" hubble's parameter"> hubble's parameter</a>, <a href="https://publications.waset.org/abstracts/search?q=ornstein-uhlenbeck%20process" title=" ornstein-uhlenbeck process "> ornstein-uhlenbeck process </a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20differential%20equations" title=" stochastic differential equations "> stochastic differential equations </a> </p> <a href="https://publications.waset.org/abstracts/116444/stochastic-variation-of-the-hubbles-parameter-using-ornstein-uhlenbeck-process" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/116444.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">201</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1552</span> A Multivariate 4/2 Stochastic Covariance Model: Properties and Applications to Portfolio Decisions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yuyang%20Cheng">Yuyang Cheng</a>, <a href="https://publications.waset.org/abstracts/search?q=Marcos%20Escobar-Anel"> Marcos Escobar-Anel</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper introduces a multivariate 4/2 stochastic covariance process generalizing the one-dimensional counterparts presented in Grasselli (2017). Our construction permits stochastic correlation not only among stocks but also among volatilities, also known as co-volatility movements, both driven by more convenient 4/2 stochastic structures. The parametrization is flexible enough to separate these types of correlation, permitting their individual study. Conditions for proper changes of measure and closed-form characteristic functions under risk-neutral and historical measures are provided, allowing for applications of the model to risk management and derivative pricing. We apply the model to an expected utility theory problem in incomplete markets. Our analysis leads to closed-form solutions for the optimal allocation and value function. Conditions are provided for well-defined solutions together with a verification theorem. Our numerical analysis highlights and separates the impact of key statistics on equity portfolio decisions, in particular, volatility, correlation, and co-volatility movements, with the latter being the least important in an incomplete market. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=stochastic%20covariance%20process" title="stochastic covariance process">stochastic covariance process</a>, <a href="https://publications.waset.org/abstracts/search?q=4%2F2%20stochastic%20volatility%20model" title=" 4/2 stochastic volatility model"> 4/2 stochastic volatility model</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20co-volatility%20movements" title=" stochastic co-volatility movements"> stochastic co-volatility movements</a>, <a href="https://publications.waset.org/abstracts/search?q=characteristic%20function" title=" characteristic function"> characteristic function</a>, <a href="https://publications.waset.org/abstracts/search?q=expected%20utility%20theory" title=" expected utility theory"> expected utility theory</a>, <a href="https://publications.waset.org/abstracts/search?q=veri%0Ccation%20theorem" title=" verication theorem"> verication theorem</a> </p> <a href="https://publications.waset.org/abstracts/153747/a-multivariate-42-stochastic-covariance-model-properties-and-applications-to-portfolio-decisions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/153747.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">152</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1551</span> Stochastic Prioritization of Dependent Actuarial Risks: Preferences among Prospects</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ezgi%20Nevruz">Ezgi Nevruz</a>, <a href="https://publications.waset.org/abstracts/search?q=Kasirga%20Yildirak"> Kasirga Yildirak</a>, <a href="https://publications.waset.org/abstracts/search?q=Ashis%20SenGupta"> Ashis SenGupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Comparing or ranking risks is the main motivating factor behind the human trait of making choices. Cumulative prospect theory (CPT) is a preference theory approach that evaluates perception and bias in decision making under risk and uncertainty. We aim to investigate the aggregate claims of different risk classes in terms of their comparability and amenability to ordering when the impact of risk perception is considered. For this aim, we prioritize the aggregate claims taken as actuarial risks by using various stochastic ordering relations. In order to prioritize actuarial risks, we use stochastic relations such as stochastic dominance and stop-loss dominance that are proposed in the frame of partial order theory. We take into account the dependency of the individual claims exposed to similar environmental risks. At first, we modify the zero-utility premium principle in order to obtain a solution for the stop-loss premium under CPT. Then, we propose a stochastic stop-loss dominance of the aggregate claims and find a relation between the stop-loss dominance and the first-order stochastic dominance under the dependence assumption by using properties of the familiar as well as some emerging multivariate claim distributions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cumulative%20prospect%20theory" title="cumulative prospect theory">cumulative prospect theory</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20order%20theory" title=" partial order theory"> partial order theory</a>, <a href="https://publications.waset.org/abstracts/search?q=risk%20perception" title=" risk perception"> risk perception</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20dominance" title=" stochastic dominance"> stochastic dominance</a>, <a href="https://publications.waset.org/abstracts/search?q=stop-loss%20dominance" title=" stop-loss dominance"> stop-loss dominance</a> </p> <a href="https://publications.waset.org/abstracts/55845/stochastic-prioritization-of-dependent-actuarial-risks-preferences-among-prospects" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55845.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">321</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1550</span> Formulating the Stochastic Finite Elements for Free Vibration Analysis of Plates with Variable Elastic Modulus</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mojtaba%20Aghamiri%20Esfahani">Mojtaba Aghamiri Esfahani</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Karkon"> Mohammad Karkon</a>, <a href="https://publications.waset.org/abstracts/search?q=Seyed%20Majid%20Hosseini%20Nezhad"> Seyed Majid Hosseini Nezhad</a>, <a href="https://publications.waset.org/abstracts/search?q=Reza%20Hosseini-Ara"> Reza Hosseini-Ara </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=stochastic%20finite%20elements" title="stochastic finite elements">stochastic finite elements</a>, <a href="https://publications.waset.org/abstracts/search?q=plate%20bending" title=" plate bending"> plate bending</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20vibration" title=" free vibration"> free vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=Monte%20Carlo" title=" Monte Carlo"> Monte Carlo</a>, <a href="https://publications.waset.org/abstracts/search?q=Neumann%20expansion%20method." title=" Neumann expansion method. "> Neumann expansion method. </a> </p> <a href="https://publications.waset.org/abstracts/45285/formulating-the-stochastic-finite-elements-for-free-vibration-analysis-of-plates-with-variable-elastic-modulus" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45285.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">394</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1549</span> Portfolio Optimization under a Hybrid Stochastic Volatility and Constant Elasticity of Variance Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jai%20Heui%20Kim">Jai Heui Kim</a>, <a href="https://publications.waset.org/abstracts/search?q=Sotheara%20Veng"> Sotheara Veng</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper studies the portfolio optimization problem for a pension fund under a hybrid model of stochastic volatility and constant elasticity of variance (CEV) using asymptotic analysis method. When the volatility component is fast mean-reverting, it is able to derive asymptotic approximations for the value function and the optimal strategy for general utility functions. Explicit solutions are given for the exponential and hyperbolic absolute risk aversion (HARA) utility functions. The study also shows that using the leading order optimal strategy results in the value function, not only up to the leading order, but also up to first order correction term. A practical strategy that does not depend on the unobservable volatility level is suggested. The result is an extension of the Merton's solution when stochastic volatility and elasticity of variance are considered simultaneously. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20analysis" title="asymptotic analysis">asymptotic analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=constant%20elasticity%20of%20variance" title=" constant elasticity of variance"> constant elasticity of variance</a>, <a href="https://publications.waset.org/abstracts/search?q=portfolio%20optimization" title=" portfolio optimization"> portfolio optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20optimal%20control" title=" stochastic optimal control"> stochastic optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20volatility" title=" stochastic volatility"> stochastic volatility</a> </p> <a href="https://publications.waset.org/abstracts/50103/portfolio-optimization-under-a-hybrid-stochastic-volatility-and-constant-elasticity-of-variance-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/50103.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">299</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1548</span> Use the Null Space to Create Starting Point for Stochastic Programming</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ghussoun%20Al-Jeiroudi">Ghussoun Al-Jeiroudi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Stochastic programming is one of the powerful technique which is used to solve real-life problems. Hence, the data of real-life problems is subject to significant uncertainty. Uncertainty is well studied and modeled by stochastic programming. Each day, problems become bigger and bigger and the need for a tool, which does deal with large scale problems, increase. Interior point method is a perfect tool to solve such problems. Interior point method is widely employed to solve the programs, which arise from stochastic programming. It is an iterative technique, so it is required a starting point. Well design starting point plays an important role in improving the convergence speed. In this paper, we propose a starting point for interior point method for multistage stochastic programming. Usually, the optimal solution of stage k+1 is used as starting point for the stage k. This point has the advantage of being close to the solution of the current program. However, it has a disadvantage; it is not in the feasible region of the current program. So, we suggest to take this point and modifying it. That is by adding to it a vector in the null space of the matrix of the unchanged constraints because the solution will change only in the null space of this matrix. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=interior%20point%20methods" title="interior point methods">interior point methods</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20programming" title=" stochastic programming"> stochastic programming</a>, <a href="https://publications.waset.org/abstracts/search?q=null%20space" title=" null space"> null space</a>, <a href="https://publications.waset.org/abstracts/search?q=starting%20points" title=" starting points"> starting points</a> </p> <a href="https://publications.waset.org/abstracts/54185/use-the-null-space-to-create-starting-point-for-stochastic-programming" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54185.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">418</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1547</span> Stochastic Programming and C-Somga: Animal Ration Formulation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Pratiksha%20Saxena">Pratiksha Saxena</a>, <a href="https://publications.waset.org/abstracts/search?q=Dipti%20Singh"> Dipti Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Neha%20Khanna"> Neha Khanna</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A self-organizing migrating genetic algorithm(C-SOMGA) is developed for animal diet formulation. This paper presents animal diet formulation using stochastic and genetic algorithm. Tri-objective models for cost minimization and shelf life maximization are developed. These objectives are achieved by combination of stochastic programming and C-SOMGA. Stochastic programming is used to introduce nutrient variability for animal diet. Self-organizing migrating genetic algorithm provides exact and quick solution and presents an innovative approach towards successful application of soft computing technique in the area of animal diet formulation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=animal%20feed%20ration" title="animal feed ration">animal feed ration</a>, <a href="https://publications.waset.org/abstracts/search?q=feed%20formulation" title=" feed formulation"> feed formulation</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20programming" title=" linear programming"> linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20programming" title=" stochastic programming"> stochastic programming</a>, <a href="https://publications.waset.org/abstracts/search?q=self-migrating%20genetic%20algorithm" title=" self-migrating genetic algorithm"> self-migrating genetic algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=C-SOMGA%20technique" title=" C-SOMGA technique"> C-SOMGA technique</a>, <a href="https://publications.waset.org/abstracts/search?q=shelf%20life%20maximization" title=" shelf life maximization"> shelf life maximization</a>, <a href="https://publications.waset.org/abstracts/search?q=cost%20minimization" title=" cost minimization"> cost minimization</a>, <a href="https://publications.waset.org/abstracts/search?q=nutrient%20maximization" title=" nutrient maximization"> nutrient maximization</a> </p> <a href="https://publications.waset.org/abstracts/35795/stochastic-programming-and-c-somga-animal-ration-formulation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35795.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">442</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1546</span> Identification of Wiener Model Using Iterative Schemes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Vikram%20Saini">Vikram Saini</a>, <a href="https://publications.waset.org/abstracts/search?q=Lillie%20Dewan"> Lillie Dewan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents the iterative schemes based on Least square, Hierarchical Least Square and Stochastic Approximation Gradient method for the Identification of Wiener model with parametric structure. A gradient method is presented for the parameter estimation of wiener model with noise conditions based on the stochastic approximation. Simulation results are presented for the Wiener model structure with different static non-linear elements in the presence of colored noise to show the comparative analysis of the iterative methods. The stochastic gradient method shows improvement in the estimation performance and provides fast convergence of the parameters estimates. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hard%20non-linearity" title="hard non-linearity">hard non-linearity</a>, <a href="https://publications.waset.org/abstracts/search?q=least%20square" title=" least square"> least square</a>, <a href="https://publications.waset.org/abstracts/search?q=parameter%20estimation" title=" parameter estimation"> parameter estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20approximation%20gradient" title=" stochastic approximation gradient"> stochastic approximation gradient</a>, <a href="https://publications.waset.org/abstracts/search?q=Wiener%20model" title=" Wiener model"> Wiener model</a> </p> <a href="https://publications.waset.org/abstracts/70632/identification-of-wiener-model-using-iterative-schemes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/70632.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">405</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1545</span> Method to Find a 蔚-Optimal Control of Stochastic Differential Equation Driven by a Brownian Motion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Francys%20Souza">Francys Souza</a>, <a href="https://publications.waset.org/abstracts/search?q=Alberto%20Ohashi"> Alberto Ohashi</a>, <a href="https://publications.waset.org/abstracts/search?q=Dorival%20Leao"> Dorival Leao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present a general solution for finding the 蔚-optimal controls for non-Markovian stochastic systems as stochastic differential equations driven by Brownian motion, which is a problem recognized as a difficult solution. The contribution appears in the development of mathematical tools to deal with modeling and control of non-Markovian systems, whose applicability in different areas is well known. The methodology used consists to discretize the problem through a random discretization. In this way, we transform an infinite dimensional problem in a finite dimensional, thereafter we use measurable selection arguments, to find a control on an explicit form for the discretized problem. Then, we prove the control found for the discretized problem is a 蔚-optimal control for the original problem. Our theory provides a concrete description of a rather general class, among the principals, we can highlight financial problems such as portfolio control, hedging, super-hedging, pairs-trading and others. Therefore, our main contribution is the development of a tool to explicitly the 蔚-optimal control for non-Markovian stochastic systems. The pathwise analysis was made through a random discretization jointly with measurable selection arguments, has provided us with a structure to transform an infinite dimensional problem into a finite dimensional. The theory is applied to stochastic control problems based on path-dependent stochastic differential equations, where both drift and diffusion components are controlled. We are able to explicitly show optimal control with our method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamic%20programming%20equation" title="dynamic programming equation">dynamic programming equation</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20control" title=" optimal control"> optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20control" title=" stochastic control"> stochastic control</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20differential%20equation" title=" stochastic differential equation"> stochastic differential equation</a> </p> <a href="https://publications.waset.org/abstracts/94746/method-to-find-a-e-optimal-control-of-stochastic-differential-equation-driven-by-a-brownian-motion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/94746.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">188</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1544</span> Stability of Stochastic Model Predictive Control for Schr枚dinger Equation with Finite Approximation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tomoaki%20Hashimoto">Tomoaki Hashimoto</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Recent technological advance has prompted significant interest in developing the control theory of quantum systems. Following the increasing interest in the control of quantum dynamics, this paper examines the control problem of Schrödinger equation because quantum dynamics is basically governed by Schrödinger equation. From the practical point of view, stochastic disturbances cannot be avoided in the implementation of control method for quantum systems. Thus, we consider here the robust stabilization problem of Schrödinger equation against stochastic disturbances. In this paper, we adopt model predictive control method in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. The objective of this study is to derive the stability criterion for model predictive control of Schrödinger equation under stochastic disturbances. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=optimal%20control" title="optimal control">optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20systems" title=" stochastic systems"> stochastic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=quantum%20systems" title=" quantum systems"> quantum systems</a>, <a href="https://publications.waset.org/abstracts/search?q=stabilization" title=" stabilization"> stabilization</a> </p> <a href="https://publications.waset.org/abstracts/62500/stability-of-stochastic-model-predictive-control-for-schrodinger-equation-with-finite-approximation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/62500.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">458</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1543</span> Optimal Production and Maintenance Policy for a Partially Observable Production System with Stochastic Demand</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Leila%20Jafari">Leila Jafari</a>, <a href="https://publications.waset.org/abstracts/search?q=Viliam%20Makis"> Viliam Makis</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the joint optimization of the economic manufacturing quantity (EMQ), safety stock level, and condition-based maintenance (CBM) is presented for a partially observable, deteriorating system subject to random failure. The demand is stochastic and it is described by a Poisson process. The stochastic model is developed and the optimization problem is formulated in the semi-Markov decision process framework. A modification of the policy iteration algorithm is developed to find the optimal policy. A numerical example is presented to compare the optimal policy with the policy considering zero safety stock. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=condition-based%20maintenance" title="condition-based maintenance">condition-based maintenance</a>, <a href="https://publications.waset.org/abstracts/search?q=economic%20manufacturing%20quantity" title=" economic manufacturing quantity"> economic manufacturing quantity</a>, <a href="https://publications.waset.org/abstracts/search?q=safety%20stock" title=" safety stock"> safety stock</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20demand" title=" stochastic demand"> stochastic demand</a> </p> <a href="https://publications.waset.org/abstracts/63628/optimal-production-and-maintenance-policy-for-a-partially-observable-production-system-with-stochastic-demand" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/63628.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">464</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1542</span> A Study on Stochastic Integral Associated with Catastrophes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Reni%20Sagayaraj">M. Reni Sagayaraj</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Anand%20Gnana%20Selvam"> S. Anand Gnana Selvam</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Reynald%20Susainathan"> R. Reynald Susainathan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=stochastic%20integrals" title="stochastic integrals">stochastic integrals</a>, <a href="https://publications.waset.org/abstracts/search?q=single%E2%80%93server%20queue%20model" title=" single鈥搒erver queue model"> single鈥搒erver queue model</a>, <a href="https://publications.waset.org/abstracts/search?q=catastrophes" title=" catastrophes"> catastrophes</a>, <a href="https://publications.waset.org/abstracts/search?q=busy%20period" title=" busy period"> busy period</a> </p> <a href="https://publications.waset.org/abstracts/21325/a-study-on-stochastic-integral-associated-with-catastrophes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/21325.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">642</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1541</span> Numerical Analysis of Laminar Mixed Convection within a Complex Geometry</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Y.%20Lasbet">Y. Lasbet</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20L.%20Boukhalkhal"> A. L. Boukhalkhal</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20Loubar"> K. Loubar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The study of mixed convection is, usually, focused on the straight channels in which the onset of the mixed convection is well defined as function of the ratio between Grashof number and Reynolds number, Gr/Re. This is not the case for a complex channel wherein the mixed convection is not sufficiently examined in the literature. Our paper focuses on the study of the mixed convection in a complex geometry in which our main contribution reveals that the critical value of the ratio Gr/Re for the onset of the mixed convection increases highly in the type of geometry contrary to the straight channel. Furthermore, the accentuated secondary flow in this geometry prevents the thermal stratification in the flow and consequently the buoyancy driven becomes negligible. To perform these objectives, a numerical study in complex geometry for several values of the ratio Gr/Re with prescribed wall heat flux (H2), was realized by using the CFD code. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=complex%20geometry" title="complex geometry">complex geometry</a>, <a href="https://publications.waset.org/abstracts/search?q=heat%20transfer" title=" heat transfer"> heat transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=laminar%20flow" title=" laminar flow"> laminar flow</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed%20convection" title=" mixed convection"> mixed convection</a>, <a href="https://publications.waset.org/abstracts/search?q=Nusselt%20number" title=" Nusselt number"> Nusselt number</a> </p> <a href="https://publications.waset.org/abstracts/35925/numerical-analysis-of-laminar-mixed-convection-within-a-complex-geometry" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35925.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">493</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1540</span> Analysis of Two Methods to Estimation Stochastic Demand in the Vehicle Routing Problem</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fatemeh%20Torfi">Fatemeh Torfi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Estimation of stochastic demand in physical distribution in general and efficient transport routs management in particular is emerging as a crucial factor in urban planning domain. It is particularly important in some municipalities such as Tehran where a sound demand management calls for a realistic analysis of the routing system. The methodology involved critically investigating a fuzzy least-squares linear regression approach (FLLRs) to estimate the stochastic demands in the vehicle routing problem (VRP) bearing in mind the customer's preferences order. A FLLR method is proposed in solving the VRP with stochastic demands. Approximate-distance fuzzy least-squares (ADFL) estimator ADFL estimator is applied to original data taken from a case study. The SSR values of the ADFL estimator and real demand are obtained and then compared to SSR values of the nominal demand and real demand. Empirical results showed that the proposed methods can be viable in solving problems under circumstances of having vague and imprecise performance ratings. The results further proved that application of the ADFL was realistic and efficient estimator to face the stochastic demand challenges in vehicle routing system management and solve relevant problems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20least-squares" title="fuzzy least-squares">fuzzy least-squares</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic" title=" stochastic"> stochastic</a>, <a href="https://publications.waset.org/abstracts/search?q=location" title=" location"> location</a>, <a href="https://publications.waset.org/abstracts/search?q=routing%20problems" title=" routing problems "> routing problems </a> </p> <a href="https://publications.waset.org/abstracts/3439/analysis-of-two-methods-to-estimation-stochastic-demand-in-the-vehicle-routing-problem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3439.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">434</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1539</span> CE Method for Development of Japan's Stochastic Earthquake Catalogue</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Babak%20Kamrani">Babak Kamrani</a>, <a href="https://publications.waset.org/abstracts/search?q=Nozar%20Kishi"> Nozar Kishi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Stochastic catalog represents the events module of the earthquake loss estimation models. It includes series of events with different magnitudes and corresponding frequencies/probabilities. For the development of the stochastic catalog, random or uniform sampling methods are used to sample the events from the seismicity model. For covering all the Magnitude Frequency Distribution (MFD), a huge number of events should be generated for the above-mentioned methods. Characteristic Event (CE) method chooses the events based on the interest of the insurance industry. We divide the MFD of each source into bins. We have chosen the bins based on the probability of the interest by the insurance industry. First, we have collected the information for the available seismic sources. Sources are divided into Fault sources, subduction, and events without specific fault source. We have developed the MFD for each of the individual and areal source based on the seismicity of the sources. Afterward, we have calculated the CE magnitudes based on the desired probability. To develop the stochastic catalog, we have introduced uncertainty to the location of the events too. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=stochastic%20catalogue" title="stochastic catalogue">stochastic catalogue</a>, <a href="https://publications.waset.org/abstracts/search?q=earthquake%20loss" title=" earthquake loss"> earthquake loss</a>, <a href="https://publications.waset.org/abstracts/search?q=uncertainty" title=" uncertainty"> uncertainty</a>, <a href="https://publications.waset.org/abstracts/search?q=characteristic%20event" title=" characteristic event"> characteristic event</a> </p> <a href="https://publications.waset.org/abstracts/63618/ce-method-for-development-of-japans-stochastic-earthquake-catalogue" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/63618.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">298</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1538</span> Evaluating Forecasts Through Stochastic Loss Order</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Wilmer%20Osvaldo%20Martinez">Wilmer Osvaldo Martinez</a>, <a href="https://publications.waset.org/abstracts/search?q=Manuel%20Dario%20Hernandez"> Manuel Dario Hernandez</a>, <a href="https://publications.waset.org/abstracts/search?q=Juan%20Manuel%20Julio"> Juan Manuel Julio</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We propose to assess the performance of k forecast procedures by exploring the distributions of forecast errors and error losses. We argue that non systematic forecast errors minimize when their distributions are symmetric and unimodal, and that forecast accuracy should be assessed through stochastic loss order rather than expected loss order, which is the way it is customarily performed in previous work. Moreover, since forecast performance evaluation can be understood as a one way analysis of variance, we propose to explore loss distributions under two circumstances; when a strict (but unknown) joint stochastic order exists among the losses of all forecast alternatives, and when such order happens among subsets of alternative procedures. In spite of the fact that loss stochastic order is stronger than loss moment order, our proposals are at least as powerful as competing tests, and are robust to the correlation, autocorrelation and heteroskedasticity settings they consider. In addition, since our proposals do not require samples of the same size, their scope is also wider, and provided that they test the whole loss distribution instead of just loss moments, they can also be used to study forecast distributions as well. We illustrate the usefulness of our proposals by evaluating a set of real world forecasts. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=forecast%20evaluation" title="forecast evaluation">forecast evaluation</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20order" title=" stochastic order"> stochastic order</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20comparison" title=" multiple comparison"> multiple comparison</a>, <a href="https://publications.waset.org/abstracts/search?q=non%20parametric%20test" title=" non parametric test"> non parametric test</a> </p> <a href="https://publications.waset.org/abstracts/167870/evaluating-forecasts-through-stochastic-loss-order" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/167870.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">89</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=stochastic%20geometry&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=stochastic%20geometry&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=stochastic%20geometry&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=stochastic%20geometry&page=5">5</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=stochastic%20geometry&page=6">6</a></li> <li class="page-item"><a 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