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

Feng, Chunrong (2021) 'Expected exit time for time-periodic stochastic differential equations and applications to stochastic resonance.', Physica D : nonlinear phenomena., 417 . p. 132815.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives 4.0.
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Publisher statement:© 2021 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:07 December 2020
Date deposited:22 February 2021
Date of first online publication:19 December 2020
Date first made open access:19 December 2021

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