{"id":9055,"date":"2025-12-12T07:02:30","date_gmt":"2025-12-12T07:02:30","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/12\/12\/2512-10256\/"},"modified":"2025-12-12T07:02:30","modified_gmt":"2025-12-12T07:02:30","slug":"2512-10256","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/12\/12\/2512-10256\/","title":{"rendered":"Error Analysis of Generalized Langevin Equations with Approximated Memory Kernels"},"content":{"rendered":"<p>    Error Analysis of Generalized Langevin Equations with Approximated Memory Kernels<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2512.10256v1 Announce Type: new<br \/>\nAbstract: We analyze prediction error in stochastic dynamical systems with memory, focusing on generalized Langevin equations (GLEs) formulated as stochastic Volterra equations. We establish that, under a strongly convex potential, trajectory discrepancies decay at a rate determined by the decay of the memory kernel and are quantitatively bounded by the estimation error of the kernel in a weighted norm. Our analysis integrates synchronized noise coupling with a Volterra comparison theorem, encompassing both subexponential and exponential kernel classes. For first-order models, we derive moment and perturbation bounds using resolvent estimates in weighted spaces. For second-order models with confining potentials, we prove contraction and stability under kernel perturbations using a hypocoercive Lyapunov-type distance. This framework accommodates non-translation-invariant kernels and white-noise forcing, explicitly linking improved kernel estimation to enhanced trajectory prediction. Numerical examples validate these theoretical findings.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Quanjun Lang, Jianfeng Lu<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2512.10256\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Error Analysis of Generalized Langevin Equations with Approximated Memory Kernels arXiv:2512.10256v1 Announce Type: new Abstract: We analyze prediction error in stochastic dynamical systems with memory, focusing on generalized Langevin equations (GLEs) formulated as stochastic Volterra equations. We establish that, under a strongly convex potential, trajectory discrepancies decay at a rate determined by the decay of [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,450,1153,451,420,112],"tags":[1819,2168,1135],"class_list":["post-9055","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-cs-na","category-math-ds","category-math-na","category-math-pr","category-stat-ml","tag-equations","tag-error","tag-kernel"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9055"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=9055"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9055\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=9055"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=9055"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=9055"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}