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Search results for: stochastic production function

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12312</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: stochastic production function</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">12312</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">12311</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">12310</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">12309</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=" veri cation theorem"> veri cation 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">12308</span> Stochastic Frontier Application for Evaluating Cost Inefficiencies in Organic Saffron</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Pawan%20Kumar%20Sharma">Pawan Kumar Sharma</a>, <a href="https://publications.waset.org/abstracts/search?q=Sudhakar%20Dwivedi"> Sudhakar Dwivedi</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20K.%20Arora"> R. K. Arora</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Saffron is one of the most precious spices grown on the earth and is cultivated in a very limited area in few countries of the world. It has also been grown as a niche crop in Kishtwar district of Jammu region of Jammu and Kashmir State of India. This paper attempts to examine the presence of cost inefficiencies in saffron production and the associated socio-economic characteristics of saffron growers in the mentioned area. Although the numbers of inputs used in cultivation of saffron were limited, still cost inefficiencies were present in its production. The net present value (NPV), internal rate of return (IRR) and profitability index (PI) of investment in five years of saffron production were INR 1120803, 95.67 % and 3.52 respectively. The estimated coefficients of saffron stochastic cost function for saffron bulbs, human labour, animal labour, manure and saffron output were positive. The saffron growers having non-farm income were more cost inefficient as compared to farmers who did not have sources of income other than farming by 0.04 %. The maximum value of cost efficiency for saffron grower was 1.69 with mean value of 1.12. The majority of farmers have low cost inefficiencies, as the highest frequency of occurrence of the predicted cost efficiency was below 1.06. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=saffron" title="saffron">saffron</a>, <a href="https://publications.waset.org/abstracts/search?q=internal%20rate%20of%20return" title=" internal rate of return"> internal rate of return</a>, <a href="https://publications.waset.org/abstracts/search?q=cost%20efficiency" title=" cost efficiency"> cost efficiency</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20frontier%20model" title=" stochastic frontier model"> stochastic frontier model</a> </p> <a href="https://publications.waset.org/abstracts/98785/stochastic-frontier-application-for-evaluating-cost-inefficiencies-in-organic-saffron" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/98785.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">153</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">12307</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&#039;s formula"> Ito&#039;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">12306</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">12305</span> A Stochastic Diffusion Process Based on the Two-Parameters Weibull Density Function</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Meriem%20Bahij">Meriem Bahij</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20Nafidi"> Ahmed Nafidi</a>, <a href="https://publications.waset.org/abstracts/search?q=Boujem%C3%A2a%20Achchab"> Boujemâa Achchab</a>, <a href="https://publications.waset.org/abstracts/search?q=S%C3%ADlvio%20M.%20A.%20Gama"> Sílvio M. A. Gama</a>, <a href="https://publications.waset.org/abstracts/search?q=Jos%C3%A9%20A.%20O.%20Matos"> José A. O. Matos</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Stochastic modeling concerns the use of probability to model real-world situations in which uncertainty is present. Therefore, the purpose of stochastic modeling is to estimate the probability of outcomes within a forecast, i.e. to be able to predict what conditions or decisions might happen under different situations. In the present study, we present a model of a stochastic diffusion process based on the bi-Weibull distribution function (its trend is proportional to the bi-Weibull probability density function). In general, the Weibull distribution has the ability to assume the characteristics of many different types of distributions. This has made it very popular among engineers and quality practitioners, who have considered it the most commonly used distribution for studying problems such as modeling reliability data, accelerated life testing, and maintainability modeling and analysis. In this work, we start by obtaining the probabilistic characteristics of this model, as the explicit expression of the process, its trends, and its distribution by transforming the diffusion process in a Wiener process as shown in the Ricciaardi theorem. Then, we develop the statistical inference of this model using the maximum likelihood methodology. Finally, we analyse with simulated data the computational problems associated with the parameters, an issue of great importance in its application to real data with the use of the convergence analysis methods. Overall, the use of a stochastic model reflects only a pragmatic decision on the part of the modeler. According to the data that is available and the universe of models known to the modeler, this model represents the best currently available description of the phenomenon under consideration. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=diffusion%20process" title="diffusion process">diffusion process</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20sampling" title=" discrete sampling"> discrete sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=likelihood%20estimation%20method" title=" likelihood estimation method"> likelihood estimation method</a>, <a href="https://publications.waset.org/abstracts/search?q=simulation" title=" simulation"> simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20diffusion%20process" title=" stochastic diffusion process"> stochastic diffusion process</a>, <a href="https://publications.waset.org/abstracts/search?q=trends%20functions" title=" trends functions"> trends functions</a>, <a href="https://publications.waset.org/abstracts/search?q=bi-parameters%20weibull%20density%20function" title=" bi-parameters weibull density function"> bi-parameters weibull density function</a> </p> <a href="https://publications.waset.org/abstracts/52569/a-stochastic-diffusion-process-based-on-the-two-parameters-weibull-density-function" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52569.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">307</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">12304</span> Pricing, Production and Inventory Policies Manufacturing under Stochastic Demand and Continuous Prices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Masoud%20Rabbani">Masoud Rabbani</a>, <a href="https://publications.waset.org/abstracts/search?q=Majede%20Smizadeh"> Majede Smizadeh</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamed%20Farrokhi-Asl"> Hamed Farrokhi-Asl</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We study jointly determining prices and production in a multiple period horizon under a general non-stationary stochastic demand with continuous prices. In some periods we need to increase capacity of production to satisfy demand. This paper presents a model to aid multi-period production capacity planning by quantifying the trade-off between product quality and production cost. The product quality is estimated as the statistical variation from the target performances obtained from the output tolerances of the production machines that manufacture the components. We consider different tolerance for different machines that use to increase capacity. The production cost is estimated as the total cost of owning and operating a production facility during the planning horizon.so capacity planning has cost that impact on price. Pricing products often turns out to be difficult to measure them because customers have a reservation price to pay that impact on price and demand. We decide to determine prices and production for periods after enhance capacity and consider reservation price to determine price. First we use an algorithm base on fuzzy set of the optimal objective function values to determine capacity planning by determine maximize interval from upper bound in minimum objectives and define weight for objectives. Then we try to determine inventory and pricing policies. We can use a lemma to solve a problem in MATLAB and find exact answer. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=price%20policy" title="price policy">price policy</a>, <a href="https://publications.waset.org/abstracts/search?q=inventory%20policy" title=" inventory policy"> inventory policy</a>, <a href="https://publications.waset.org/abstracts/search?q=capacity%20planning" title=" capacity planning"> capacity planning</a>, <a href="https://publications.waset.org/abstracts/search?q=product%20quality" title=" product quality"> product quality</a>, <a href="https://publications.waset.org/abstracts/search?q=epsilon%20-constraint" title=" epsilon -constraint"> epsilon -constraint</a> </p> <a href="https://publications.waset.org/abstracts/30981/pricing-production-and-inventory-policies-manufacturing-under-stochastic-demand-and-continuous-prices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30981.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">569</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">12303</span> On Differential Growth Equation to Stochastic Growth Model Using Hyperbolic Sine Function in Height/Diameter Modeling of Pines</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20O.%20Oyamakin">S. O. Oyamakin</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20U.%20Chukwu"> A. U. Chukwu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Richard's growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richard's growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richard's growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richard's nonlinear growth models better than the classical Richard's growth model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=height" title="height">height</a>, <a href="https://publications.waset.org/abstracts/search?q=Dbh" title=" Dbh"> Dbh</a>, <a href="https://publications.waset.org/abstracts/search?q=forest" title=" forest"> forest</a>, <a href="https://publications.waset.org/abstracts/search?q=Pinus%20caribaea" title=" Pinus caribaea"> Pinus caribaea</a>, <a href="https://publications.waset.org/abstracts/search?q=hyperbolic" title=" hyperbolic"> hyperbolic</a>, <a href="https://publications.waset.org/abstracts/search?q=Richard%27s" title=" Richard&#039;s"> Richard&#039;s</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic" title=" stochastic"> stochastic</a> </p> <a href="https://publications.waset.org/abstracts/17738/on-differential-growth-equation-to-stochastic-growth-model-using-hyperbolic-sine-function-in-heightdiameter-modeling-of-pines" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17738.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">480</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">12302</span> Multi-Period Supply Chain Design under Uncertainty</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Amir%20Azaron">Amir Azaron</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this research, a stochastic programming approach is developed for designing supply chains with uncertain parameters. Demands and selling prices of products at markets are considered as the uncertain parameters. The proposed mathematical model will be multi-period two-stage stochastic programming, which takes into account the selection of retailer sites, suppliers, production levels, inventory levels, transportation modes to be used for shipping goods, and shipping quantities among the entities of the supply chain network. The objective function is to maximize the chain’s net present value. In order to maximize the chain’s NPV, the sum of first-stage investment costs on retailers, and the expected second-stage processing, inventory-holding and transportation costs should be kept as low as possible over multiple periods. The effects of supply uncertainty where suppliers are unreliable will also be investigated on the efficiency of the supply chain. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=supply%20chain%20management" title="supply chain management">supply chain management</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=multiobjective%20programming" title=" multiobjective programming"> multiobjective programming</a>, <a href="https://publications.waset.org/abstracts/search?q=inventory%20control" title=" inventory control"> inventory control</a> </p> <a href="https://publications.waset.org/abstracts/66297/multi-period-supply-chain-design-under-uncertainty" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/66297.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">295</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">12301</span> Stochastic Variation of the Hubble&#039;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’s 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&#039;s parameter"> hubble&#039;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">12300</span> Heteroscedastic Parametric and Semiparametric Smooth Coefficient Stochastic Frontier Application to Technical Efficiency Measurement</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rebecca%20Owusu%20Coffie">Rebecca Owusu Coffie</a>, <a href="https://publications.waset.org/abstracts/search?q=Atakelty%20Hailu"> Atakelty Hailu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Variants of production frontier models have emerged, however, only a limited number of them are applied in empirical research. Hence the effects of these alternative frontier models are not well understood, particularly within sub-Saharan Africa. In this paper, we apply recent advances in the production frontier to examine levels of technical efficiency and efficiency drivers. Specifically, we compare the heteroscedastic parametric and the semiparametric stochastic smooth coefficient (SPSC) models. Using rice production data from Ghana, our empirical estimates reveal that alternative specification of efficiency estimators results in either downward or upward bias in the technical efficiency estimates. Methodologically, we find that the SPSC model is more suitable and generates high-efficiency estimates. Within the parametric framework, we find that parameterization of both the mean and variance of the pre-truncated function is the best model. For the drivers of technical efficiency, we observed that longer farm distances increase inefficiency through a reduction in labor productivity. High soil quality, however, increases productivity through increased land productivity. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=pre-truncated" title="pre-truncated">pre-truncated</a>, <a href="https://publications.waset.org/abstracts/search?q=rice%20production" title=" rice production"> rice production</a>, <a href="https://publications.waset.org/abstracts/search?q=smooth%20coefficient" title=" smooth coefficient"> smooth coefficient</a>, <a href="https://publications.waset.org/abstracts/search?q=technical%20efficiency" title=" technical efficiency"> technical efficiency</a> </p> <a href="https://publications.waset.org/abstracts/59500/heteroscedastic-parametric-and-semiparametric-smooth-coefficient-stochastic-frontier-application-to-technical-efficiency-measurement" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59500.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">444</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">12299</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">12298</span> A Reactive Flexible Job Shop Scheduling Model in a Stochastic Environment</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Majid%20Khalili">Majid Khalili</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamed%20Tayebi"> Hamed Tayebi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper considers a stochastic flexible job-shop scheduling (SFJSS) problem in the presence of production disruptions, and reactive scheduling is implemented in order to find the optimal solution under uncertainty. In this problem, there are two main disruptions including machine failure which influences operation time, and modification or cancellation of the order delivery date during production. In order to decrease the negative effects of these difficulties, two derived strategies from reactive scheduling are used; the first one is relevant to being able to allocate multiple machine to each job, and the other one is related to being able to select the best alternative process from other job while some disruptions would be created in the processes of a job. For this purpose, a Mixed Integer Linear Programming model is proposed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=flexible%20job-shop%20scheduling" title="flexible job-shop scheduling">flexible job-shop scheduling</a>, <a href="https://publications.waset.org/abstracts/search?q=reactive%20scheduling" title=" reactive scheduling"> reactive scheduling</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20environment" title=" stochastic environment"> stochastic environment</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed%20integer%20linear%20programming" title=" mixed integer linear programming"> mixed integer linear programming</a> </p> <a href="https://publications.waset.org/abstracts/69932/a-reactive-flexible-job-shop-scheduling-model-in-a-stochastic-environment" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/69932.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">360</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">12297</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’s 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">12296</span> Stability of Hybrid Stochastic Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Manlika%20Ratchagit">Manlika Ratchagit</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=robust%20mean%20square%20stability" title="robust mean square stability">robust mean square stability</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete-time%20stochastic%20systems" title=" discrete-time stochastic systems"> discrete-time stochastic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20systems" title=" hybrid systems"> hybrid systems</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20time-varying%20delays" title=" interval time-varying delays"> interval time-varying delays</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov%20functional" title=" Lyapunov functional"> Lyapunov functional</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20matrix%20inequalities" title=" linear matrix inequalities"> linear matrix inequalities</a> </p> <a href="https://publications.waset.org/abstracts/20283/stability-of-hybrid-stochastic-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20283.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">485</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">12295</span> New Results on Stability of Hybrid Stochastic Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Manlika%20Rajchakit">Manlika Rajchakit</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=robust%20mean%20square%20stability" title="robust mean square stability">robust mean square stability</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete-time%20stochastic%20systems" title=" discrete-time stochastic systems"> discrete-time stochastic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20systems" title=" hybrid systems"> hybrid systems</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20time-varying%20delays" title=" interval time-varying delays"> interval time-varying delays</a>, <a href="https://publications.waset.org/abstracts/search?q=lyapunov%20functional" title=" lyapunov functional"> lyapunov functional</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20matrix%20inequalities" title=" linear matrix inequalities"> linear matrix inequalities</a> </p> <a href="https://publications.waset.org/abstracts/19809/new-results-on-stability-of-hybrid-stochastic-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19809.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">429</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">12294</span> Best Resource Recommendation for a Stochastic Process</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Likewin%20Thomas">Likewin Thomas</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20V.%20Manoj%20Kumar"> M. V. Manoj Kumar</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20Annappa"> B. Annappa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of this study was to develop an Artificial Neural Network0 s recommendation model for an online process using the complexity of load, performance, and average servicing time of the resources. Here, the proposed model investigates the resource performance using stochastic gradient decent method for learning ranking function. A probabilistic cost function is implemented to identify the optimal θ values (load) on each resource. Based on this result the recommendation of resource suitable for performing the currently executing task is made. The test result of CoSeLoG project is presented with an accuracy of 72.856%. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=ADALINE" title="ADALINE">ADALINE</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20network" title=" neural network"> neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=gradient%20decent" title=" gradient decent"> gradient decent</a>, <a href="https://publications.waset.org/abstracts/search?q=process%20mining" title=" process mining"> process mining</a>, <a href="https://publications.waset.org/abstracts/search?q=resource%20behaviour" title=" resource behaviour"> resource behaviour</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20regression%20model" title=" polynomial regression model"> polynomial regression model</a> </p> <a href="https://publications.waset.org/abstracts/45008/best-resource-recommendation-for-a-stochastic-process" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45008.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">390</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">12293</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">María L. Jalón</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">12292</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">12291</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">12290</span> Deterministic and Stochastic Modeling of a Micro-Grid Management for Optimal Power Self-Consumption</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=D.%20Calogine">D. Calogine</a>, <a href="https://publications.waset.org/abstracts/search?q=O.%20Chau"> O. Chau</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Dotti"> S. Dotti</a>, <a href="https://publications.waset.org/abstracts/search?q=O.%20Ramiarinjanahary"> O. Ramiarinjanahary</a>, <a href="https://publications.waset.org/abstracts/search?q=P.%20Rasoavonjy"> P. Rasoavonjy</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Tovondahiniriko"> F. Tovondahiniriko</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Mafate is a natural circus in the north-western part of Reunion Island, without an electrical grid and road network. A micro-grid concept is being experimented in this area, composed of a photovoltaic production combined with electrochemical batteries, in order to meet the local population for self-consumption of electricity demands. This work develops a discrete model as well as a stochastic model in order to reach an optimal equilibrium between production and consumptions for a cluster of houses. The management of the energy power leads to a large linearized programming system, where the time interval of interest is 24 hours The experimental data are solar production, storage energy, and the parameters of the different electrical devices and batteries. The unknown variables to evaluate are the consumptions of the various electrical services, the energy drawn from and stored in the batteries, and the inhabitants’ planning wishes. The objective is to fit the solar production to the electrical consumption of the inhabitants, with an optimal use of the energies in the batteries by satisfying as widely as possible the users' planning requirements. In the discrete model, the different parameters and solutions of the linear programming system are deterministic scalars. Whereas in the stochastic approach, the data parameters and the linear programming solutions become random variables, then the distributions of which could be imposed or established by estimation from samples of real observations or from samples of optimal discrete equilibrium solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=photovoltaic%20production" title="photovoltaic production">photovoltaic production</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20consumption" title=" power consumption"> power consumption</a>, <a href="https://publications.waset.org/abstracts/search?q=battery%20storage%20resources" title=" battery storage resources"> battery storage resources</a>, <a href="https://publications.waset.org/abstracts/search?q=random%20variables" title=" random variables"> random variables</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20modeling" title=" stochastic modeling"> stochastic modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=estimations%20of%20probability%20distributions" title=" estimations of probability distributions"> estimations of probability distributions</a>, <a href="https://publications.waset.org/abstracts/search?q=mixed%20integer%20linear%20programming" title=" mixed integer linear programming"> mixed integer linear programming</a>, <a href="https://publications.waset.org/abstracts/search?q=smart%20micro-grid" title=" smart micro-grid"> smart micro-grid</a>, <a href="https://publications.waset.org/abstracts/search?q=self-consumption%20of%20electricity." title=" self-consumption of electricity."> self-consumption of electricity.</a> </p> <a href="https://publications.waset.org/abstracts/156042/deterministic-and-stochastic-modeling-of-a-micro-grid-management-for-optimal-power-self-consumption" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/156042.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">110</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">12289</span> Increasing Performance of Autopilot Guided Small Unmanned Helicopter</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tugrul%20Oktay">Tugrul Oktay</a>, <a href="https://publications.waset.org/abstracts/search?q=Mehmet%20Konar"> Mehmet Konar</a>, <a href="https://publications.waset.org/abstracts/search?q=Mustafa%20Soylak"> Mustafa Soylak</a>, <a href="https://publications.waset.org/abstracts/search?q=Firat%20Sal"> Firat Sal</a>, <a href="https://publications.waset.org/abstracts/search?q=Murat%20Onay"> Murat Onay</a>, <a href="https://publications.waset.org/abstracts/search?q=Orhan%20Kizilkaya"> Orhan Kizilkaya</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, autonomous performance of a small manufactured unmanned helicopter is tried to be increased. For this purpose, a small unmanned helicopter is manufactured in Erciyes University, Faculty of Aeronautics and Astronautics. It is called as ZANKA-Heli-I. For performance maximization, autopilot parameters are determined via minimizing a cost function consisting of flight performance parameters such as settling time, rise time, overshoot during trajectory tracking. For this purpose, a stochastic optimization method named as simultaneous perturbation stochastic approximation is benefited. Using this approach, considerable autonomous performance increase (around %23) is obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=small%20helicopters" title="small helicopters">small helicopters</a>, <a href="https://publications.waset.org/abstracts/search?q=hierarchical%20control" title=" hierarchical control"> hierarchical control</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20optimization" title=" stochastic optimization"> stochastic optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=autonomous%20performance%20maximization" title=" autonomous performance maximization"> autonomous performance maximization</a>, <a href="https://publications.waset.org/abstracts/search?q=autopilots" title=" autopilots"> autopilots</a> </p> <a href="https://publications.waset.org/abstracts/35994/increasing-performance-of-autopilot-guided-small-unmanned-helicopter" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35994.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">582</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">12288</span> A Stochastic Approach to Extreme Wind Speeds Conditions on a Small Axial Wind Turbine</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nkongho%20Ayuketang%20Arreyndip">Nkongho Ayuketang Arreyndip</a>, <a href="https://publications.waset.org/abstracts/search?q=Ebobenow%20Joseph"> Ebobenow Joseph</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, to model a real life wind turbine, a probabilistic approach is proposed to model the dynamics of the blade elements of a small axial wind turbine under extreme stochastic wind speeds conditions. It was found that the power and the torque probability density functions even though decreases at these extreme wind speeds but are not infinite. Moreover, we also found that it is possible to stabilize the power coefficient (stabilizing the output power) above rated wind speeds by turning some control parameters. This method helps to explain the effect of turbulence on the quality and quantity of the harness power and aerodynamic torque. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=probability" title="probability">probability</a>, <a href="https://publications.waset.org/abstracts/search?q=probability%20density%20function" title=" probability density function"> probability density function</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic" title=" stochastic"> stochastic</a>, <a href="https://publications.waset.org/abstracts/search?q=turbulence" title=" turbulence"> turbulence</a> </p> <a href="https://publications.waset.org/abstracts/34813/a-stochastic-approach-to-extreme-wind-speeds-conditions-on-a-small-axial-wind-turbine" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/34813.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">587</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">12287</span> A Multi-Criteria Model for Scheduling of Stochastic Single Machine Problem with Outsourcing and Solving It through Application of Chance Constrained </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Homa%20Ghave">Homa Ghave</a>, <a href="https://publications.waset.org/abstracts/search?q=Parmis%20Shahmaleki"> Parmis Shahmaleki</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a new multi-criteria stochastic mathematical model for a single machine scheduling with outsourcing allowed. There are multiple jobs processing in batch. For each batch, all of job or a quantity of it can be outsourced. The jobs have stochastic processing time and lead time and deterministic due dates arrive randomly. Because of the stochastic inherent of processing time and lead time, we use the chance constrained programming for modeling the problem. First, the problem is formulated in form of stochastic programming and then prepared in a form of deterministic mixed integer linear programming. The objectives are considered in the model to minimize the maximum tardiness and outsourcing cost simultaneously. Several procedures have been developed to deal with the multi-criteria problem. In this paper, we utilize the concept of satisfaction functions to increases the manager’s preference. The proposed approach is tested on instances where the random variables are normally distributed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=single%20machine%20scheduling" title="single machine scheduling">single machine scheduling</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-criteria%20mathematical%20model" title=" multi-criteria mathematical model"> multi-criteria mathematical model</a>, <a href="https://publications.waset.org/abstracts/search?q=outsourcing%20strategy" title=" outsourcing strategy"> outsourcing strategy</a>, <a href="https://publications.waset.org/abstracts/search?q=uncertain%20lead%20times%20and%20processing%20times" title=" uncertain lead times and processing times"> uncertain lead times and processing times</a>, <a href="https://publications.waset.org/abstracts/search?q=chance%20constrained%20programming" title=" chance constrained programming"> chance constrained programming</a>, <a href="https://publications.waset.org/abstracts/search?q=satisfaction%20function" title=" satisfaction function"> satisfaction function</a> </p> <a href="https://publications.waset.org/abstracts/43585/a-multi-criteria-model-for-scheduling-of-stochastic-single-machine-problem-with-outsourcing-and-solving-it-through-application-of-chance-constrained" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/43585.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">264</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">12286</span> Measurement of CES Production Functions Considering Energy as an Input</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Donglan%20Zha">Donglan Zha</a>, <a href="https://publications.waset.org/abstracts/search?q=Jiansong%20Si"> Jiansong Si</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Because of its flexibility, CES attracts much interest in economic growth and programming models, and the macroeconomics or micro-macro models. This paper focuses on the development, estimating methods of CES production function considering energy as an input. We leave for future research work of relaxing the assumption of constant returns to scale, the introduction of potential input factors, and the generalization method of the optimal nested form of multi-factor production functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bias%20of%20technical%20change" title="bias of technical change">bias of technical change</a>, <a href="https://publications.waset.org/abstracts/search?q=CES%20production%20function" title=" CES production function"> CES production function</a>, <a href="https://publications.waset.org/abstracts/search?q=elasticity%20of%20substitution" title=" elasticity of substitution"> elasticity of substitution</a>, <a href="https://publications.waset.org/abstracts/search?q=energy%20input" title=" energy input"> energy input</a> </p> <a href="https://publications.waset.org/abstracts/52588/measurement-of-ces-production-functions-considering-energy-as-an-input" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52588.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">282</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">12285</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">12284</span> Synthesis of Filtering in Stochastic Systems on Continuous-Time Memory Observations in the Presence of Anomalous Noises</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Rozhkova">S. Rozhkova</a>, <a href="https://publications.waset.org/abstracts/search?q=O.%20Rozhkova"> O. Rozhkova</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Harlova"> A. Harlova</a>, <a href="https://publications.waset.org/abstracts/search?q=V.%20Lasukov"> V. Lasukov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We have conducted the optimal synthesis of root-mean-squared objective filter to estimate the state vector in the case if within the observation channel with memory the anomalous noises with unknown mathematical expectation are complement in the function of the regular noises. The synthesis has been carried out for linear stochastic systems of continuous-time. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=mathematical%20expectation" title="mathematical expectation">mathematical expectation</a>, <a href="https://publications.waset.org/abstracts/search?q=filtration" title=" filtration"> filtration</a>, <a href="https://publications.waset.org/abstracts/search?q=anomalous%20noise" title=" anomalous noise"> anomalous noise</a>, <a href="https://publications.waset.org/abstracts/search?q=memory" title=" memory"> memory</a> </p> <a href="https://publications.waset.org/abstracts/28832/synthesis-of-filtering-in-stochastic-systems-on-continuous-time-memory-observations-in-the-presence-of-anomalous-noises" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/28832.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">247</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">12283</span> Modelling High-Frequency Crude Oil Dynamics Using Affine and Non-Affine Jump-Diffusion Models</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Katja%20Ignatieva">Katja Ignatieva</a>, <a href="https://publications.waset.org/abstracts/search?q=Patrick%20Wong"> Patrick Wong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We investigated the dynamics of high frequency energy prices, including crude oil and electricity prices. The returns of underlying quantities are modelled using various parametric models such as stochastic framework with jumps and stochastic volatility (SVCJ) as well as non-parametric alternatives, which are purely data driven and do not require specification of the drift or the diffusion coefficient function. Using different statistical criteria, we investigate the performance of considered parametric and nonparametric models in their ability to forecast price series and volatilities. Our models incorporate possible seasonalities in the underlying dynamics and utilise advanced estimation techniques for the dynamics of energy prices. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=stochastic%20volatility" title="stochastic volatility">stochastic volatility</a>, <a href="https://publications.waset.org/abstracts/search?q=affine%20jump-diffusion%20models" title=" affine jump-diffusion models"> affine jump-diffusion models</a>, <a href="https://publications.waset.org/abstracts/search?q=high%20frequency%20data" title=" high frequency data"> high frequency data</a>, <a href="https://publications.waset.org/abstracts/search?q=model%20specification" title=" model specification"> model specification</a>, <a href="https://publications.waset.org/abstracts/search?q=markov%20chain%20monte%20carlo" title=" markov chain monte carlo"> markov chain monte carlo</a> </p> <a href="https://publications.waset.org/abstracts/159124/modelling-high-frequency-crude-oil-dynamics-using-affine-and-non-affine-jump-diffusion-models" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/159124.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">104</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%20production%20function&amp;page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=stochastic%20production%20function&amp;page=3">3</a></li> <li class="page-item"><a class="page-link" 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