Document Zbl 07982497

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Phys. A, Math. Theor.</a> <a href="/?q=in%3A523330" title="Articles in this Issue">58, No. 4, Article ID 045001, 27 p. (2025)</a>. </div> <div class="abstract">Summary: In this work we consider a generalised Ornstein-Uhlenbeck (O-U) process for a stochastically driven particle in an harmonic potential which is governed by a Fokker-Planck equation in the presence of a memory kernel. We analyse the probability density function, the mean and the mean squared displacement (MSD) by employing the subordination approach connecting the operational time of the process with the (generalised) laboratory time. We provide analytical results for the mean and the MSD in case of a power-law memory kernel which corresponds to the fractional O-U process. The generalised O-U process in the presence of Poissonian resetting is also investigated by using the renewal equation approach, and the nonequilibrium stationary state approached in the long time limit is obtained. The analytical results are confirmed by numerical simulations based on the coupled Langevin equations.<br class="zbmathjax-paragraph">© 2025 The Author(s). Published by IOP Publishing Ltd</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A82-XX" title="MSC2020">82-XX</a> </td> <td class="space"> Statistical mechanics, structure of matter </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35-XX" title="MSC2020">35-XX</a> </td> <td class="space"> Partial differential equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AOrnstein-Uhlenbeck+process">Ornstein-Uhlenbeck process</a>; <a href="/?q=ut%3Asubordination">subordination</a>; <a href="/?q=ut%3Astochastic+resetting">stochastic resetting</a>; <a href="/?q=ut%3Anonequilibrium+stationary+state">nonequilibrium stationary state</a></div> <div class="software"> <h3>Software:</h3><a href="/software/20907">ML</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07982497" data-ciurl="/ci/07982497" data-biburl="/bibtex/07982497.bib" data-amsurl="/amsrefs/07982497.bib" data-xmlurl="/xml/07982497.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07982497.pdf" title="Zbl 07982497 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1088/1751-8121/ada748" aria-label="DOI for “Generalised Ornstein-Uhlenbeck process: memory effects and resetting”" title="10.1088/1751-8121/ada748">DOI</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Brown, R., A brief account of microscopical observations on the particles contained in the pollen of plants and on the general existence of active molecules in organic and inorganic bodies, Phil. 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