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

PHYSICA D-NONLINEAR PHENOMENA

卷:417

Article

Feng, Chunrong¹  Zhao, Huaizhong^1,2  Zhong, Johnny³ 

[1] Univ Durham, Dept Math Sci, Durham DH1 3LE, England

[2] Shandong Univ, Res Ctr Math & Interdisciplinary Sci, Qingdao 266237, Peoples R China

[3] Loughborough Univ, Dept Math Sci, Loughborough LE11 3TU, Leics, England

关键词: Expected exit time;    Time-inhomogeneous Markov processes;    Feynman-Kac duality;    Stochastic resonance;    Locally Lipschitz;    Time-periodic parabolic partial differential;    equations;   

DOI  :  10.1016/j.physd.2020.132815

来源: Elsevier

【 摘 要 】

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. (c) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

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