Favard separation method for almost periodic stochastic differential equations

TL;DR

This paper extends Favard's separation method to stochastic differential equations, establishing new theorems for almost periodic solutions in distribution, blending classical techniques with stochastic analysis.

Contribution

It introduces Favard and Amerio type theorems for stochastic differential equations using separation and almost periodicity in distribution.

Findings

Established Favard and Amerio type theorems for stochastic differential equations.

Extended classical almost periodic solution methods to stochastic contexts.

Provided a framework for analyzing almost periodic solutions in distribution.

Abstract

Favard separation method is an important means to study almost periodic solutions to linear differential equations; later, Amerio applied Favard's idea to nonlinear differential equations. In this paper, by appropriate choosing separation and almost periodicity in distribution sense, we obtain the Favard and Amerio type theorems for stochastic differential equations.