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Expected exit time for time-periodic stochastic differential equations and applications to stochastic resonance

Feng, Chunrong; Zhao, Huaizhong; Zhong, Johnny

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Authors

Johnny Zhong



Abstract

In this paper, we derive a parabolic partial differential equation for the expected exit time of non-autonomous time-periodic non-degenerate stochastic differential equations. This establishes a Feynman–Kac duality between expected exit time of time-periodic stochastic differential equations and time-periodic solutions of parabolic partial differential equations. Casting the time-periodic solution of the parabolic partial differential equation as a fixed point problem and a convex optimisation problem, we give sufficient conditions in which the partial differential equation is well-posed in a weak and classical sense. With no known closed formulae for the expected exit time, we show our method can be readily implemented by standard numerical schemes. With relatively weak conditions (e.g. locally Lipschitz coefficients), the method in this paper is applicable to wide range of physical systems including weakly dissipative systems. Particular applications towards stochastic resonance will be discussed.

Citation

Feng, C., Zhao, H., & Zhong, J. (2021). Expected exit time for time-periodic stochastic differential equations and applications to stochastic resonance. Physica D: Nonlinear Phenomena, 417, https://doi.org/10.1016/j.physd.2020.132815

Journal Article Type Article
Acceptance Date Dec 7, 2020
Online Publication Date Dec 19, 2020
Publication Date 2021-03
Deposit Date Jan 5, 2021
Publicly Available Date Dec 19, 2021
Journal Physica D: Nonlinear Phenomena
Print ISSN 0167-2789
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 417
DOI https://doi.org/10.1016/j.physd.2020.132815

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