Affine Periodic Solutions of Stochastic Differential Equations

TL;DR

This paper investigates the existence and stability of affine periodic solutions in stochastic differential equations, providing theoretical criteria and applying Lyapunov methods to establish their properties.

Contribution

It introduces new criteria for the existence and stability of affine periodic solutions in stochastic systems, extending classical results with stochastic analysis techniques.

Findings

Established a law of large numbers for stochastic affine periodic systems

Proved the existence of affine periodic solutions in distribution

Demonstrated asymptotic stability of these solutions using Lyapunov methods

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.