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Sharp asymptotic estimates for expectations, probabilities, and mean first passage times in stochastic systems with small noise
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Grafke, Tobias, Schäfer, Tobias and Vanden‐Eijnden, Eric (2024) Sharp asymptotic estimates for expectations, probabilities, and mean first passage times in stochastic systems with small noise. Communications on Pure and Applied Mathematics, 77 (4). pp. 2268-2330. doi:10.1002/cpa.22177 ISSN 0010-3640.
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Official URL: http://doi.org/10.1002/cpa.22177
Abstract
Freidlin-Wentzell theory of large deviations can be used to compute the likelihood of extreme or rare events in stochastic dynamical systems via the solution of an optimization problem. The approach gives exponential estimates that often need to be refined via calculation of a prefactor. Here it is shown how to perform these computations in practice. Specifically, sharp asymptotic estimates are derived for expectations, probabilities, and mean first passage times in a form that is geared towards numerical purposes: they require solving well-posed matrix Riccati equations involving the minimizer of the Freidlin-Wentzell action as input, either forward or backward in time with appropriate initial or final conditions tailored to the estimate at hand. The usefulness of our approach is illustrated on several examples. In particular, invariant measure probabilities and mean first passage times are calculated in models involving stochastic partial differential equations of reaction-advection-diffusion type.
Item Type: | Journal Article | ||||||||||||||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Stochastic systems , Asymptotic expansions, Probabilities, Large deviations | ||||||||||||||||||||||||
Journal or Publication Title: | Communications on Pure and Applied Mathematics | ||||||||||||||||||||||||
Publisher: | John Wiley & Sons | ||||||||||||||||||||||||
ISSN: | 0010-3640 | ||||||||||||||||||||||||
Official Date: | April 2024 | ||||||||||||||||||||||||
Dates: |
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Volume: | 77 | ||||||||||||||||||||||||
Number: | 4 | ||||||||||||||||||||||||
Page Range: | pp. 2268-2330 | ||||||||||||||||||||||||
DOI: | 10.1002/cpa.22177 | ||||||||||||||||||||||||
Status: | Peer Reviewed | ||||||||||||||||||||||||
Publication Status: | Published | ||||||||||||||||||||||||
Re-use Statement: | This is the peer reviewed version of the following article: Grafke, T., Schäfer, T. and Vanden-Eijnden, E. (2023), Sharp asymptotic estimates for expectations, probabilities, and mean first passage times in stochastic systems with small noise. Comm. Pure Appl. Math. which has been published in final form at http://doi.org/10.1002/cpa.22177. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited | ||||||||||||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||||||||
Copyright Holders: | © 2023 Wiley Periodicals LLC. | ||||||||||||||||||||||||
Date of first compliant deposit: | 13 October 2023 | ||||||||||||||||||||||||
RIOXX Funder/Project Grant: |
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