Mean square direct integration of linear stochastic delay differential equations

Mean square direct integration of linear stochastic delay differential equations | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 1 December 2025 V1 Latest version Share on Mean square direct integration of linear stochastic delay differential equations Authors : Gergő Fodor 0009-0003-5095-489X [email protected] and Dániel Bachrathy Authors Info & Affiliations https://doi.org/10.22541/au.176458878.85175765/v1 217 views 170 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Studying the stability, steady-state behavior, and transient responses of stochastic delay differential equations presents significant numerical challenges. The Monte Carlo method, commonly used to estimate statistical properties, relies on averaging over numerous simulated trajectories. While straightforward, this approach is computationally intensive and often slow to converge, especially when estimating higher-order moments. We propose a more efficient and accurate alternative: a direct integration framework for the mean square dynamics of the system. The presented Mean Square Direct Integration (MSDI) method is based on the Euler-Maruyama scheme and directly captures the evolution of second-order moments, such as variance and standard deviation. This enables the assessment of fluctuations around the mean trajectory without computing an ensemble of sample paths. Numerical experiments demonstrate that MSDI achieves higher accuracy at significantly lower computational cost than traditional Monte Carlo simulations. Supplementary Material File (msdi_wiley.pdf) Download 2.61 MB Information & Authors Information Version history V1 Version 1 01 December 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords monte carlo simulation numerical methods stochastic delay differential equations stochastic systems Authors Affiliations Gergő Fodor 0009-0003-5095-489X [email protected] Budapesti Muszaki es Gazdasagtudomanyi Egyetem Muszaki Mechanikai Tanszek View all articles by this author Dániel Bachrathy Budapesti Muszaki es Gazdasagtudomanyi Egyetem Muszaki Mechanikai Tanszek View all articles by this author Metrics & Citations Metrics Article Usage 217 views 170 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Gergő Fodor, Dániel Bachrathy. Mean square direct integration of linear stochastic delay differential equations. Authorea . 01 December 2025. DOI: https://doi.org/10.22541/au.176458878.85175765/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. 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