LaSalle-type stationary oscillation principle for stochastic affine periodic systems

Abstract

In this paper, we establish a LaSalle-type stationary oscillation principle to obtain the existence and stability of affine periodic solutions in distribution for stochastic differential equations. As applications, we show the existence and asymptotic stability of stochastic affine periodic solutions in distribution via Lyapunov’s method.

Periodic solutions in distribution for stochastic lattice differential equations

“…In the past decade, many works have been devoted to study periodicity of SDEs. For the existence of periodic solutions for finite-dimensional stochastic systems, we refer the reader to [5,9,10,11,12,16,17,18,28].…”