The paper is dedicated to studying the problem of Poisson stability (in particular stationarity,
periodicity, quasi-periodicity, Bohr almost periodicity, Bohr almost automorphy, Birkhoff …

In this paper, we study the smooth Wong-Zakai approximations given by a stochastic
process via Wiener shift and mollifier of Brownian motions. We show that solutions of …

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 …

In this paper, we define random quasi-periodic paths for random dynamical systems and
quasi-periodic measures for Markovian semigroups. We give a sufficient condition for the …

We study stochastic resonance in an over-damped approximation of the stochastic Duffing
oscillator from a random dynamical systems point of view. We analyse this problem in the …

In this paper, we discuss the numerical approximation of random periodic solutions of
stochastic differential equations (SDEs) with multiplicative noise. We prove the existence of …

In this paper, we study the existence and uniqueness of the random periodic solution for a
stochastic differential equation with a one-sided Lipschitz condition (also known as …

This work focuses on the numerical approximations of random periodic solutions of
stochastic differential equations (SDEs). Under non-globally Lipschitz conditions, we prove …

Periodic phenomena such as oscillation have been studied for many years. In this paper, we
verify the stochastic version of Levinson's conjecture, which confirmed the existence of …

Periodic measures are the time-periodic counterpart to invariant measures for dynamical
systems and can be used to characterise the long-term periodic behaviour of stochastic …