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Expected exit time for time-periodic stochastic differential equations and applications to stochastic resonance (2020)
Journal Article
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

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-... Read More about Expected exit time for time-periodic stochastic differential equations and applications to stochastic resonance.

A sufficient and necessary condition of PS-ergodicity of periodic measures and generated ergodic upper expectations (2020)
Journal Article
Feng, C., Qu, B., & Zhao, H. (2020). A sufficient and necessary condition of PS-ergodicity of periodic measures and generated ergodic upper expectations. Nonlinearity, 33(10), https://doi.org/10.1088/1361-6544/ab9584

This paper contains two parts. In the first part, we study the ergodicity of periodic measures of random dynamical systems on a separable Banach space. We obtain that the periodic measure of the continuous time skew-product dynamical system generated... Read More about A sufficient and necessary condition of PS-ergodicity of periodic measures and generated ergodic upper expectations.

Random periodic processes, periodic measures and ergodicity (2020)
Journal Article
Feng, C., & Zhao, H. (2020). Random periodic processes, periodic measures and ergodicity. Journal of Differential Equations, 269(9), 7382-7428. https://doi.org/10.1016/j.jde.2020.05.034

Ergodicity of random dynamical systems with a periodic measure is obtained on a Polish space. In the Markovian case, the idea of Poincaré sections is introduced. It is proved that if the periodic measure is PS-ergodic, then it is ergodic. Moreover, i... Read More about Random periodic processes, periodic measures and ergodicity.