Affine Periodic Solutions of Stochastic Differential Equations

Abstract

For stochastic affine periodic systems, we establish a law of large numbers including Halanay-type criterion and a LaSalle-type stationary oscillation principle to obtain the existence and stability of affine periodic solutions in distribution. As applications, we show the existence and asymptotic stability of stochastic affine periodic solutions in distribution via Lyapunov's method.