Almost Periodic Solutions and Stable Solutions for Stochastic Differential Equations

TL;DR

This paper explores the connection between stability and almost periodicity in solutions of stochastic differential equations, using Lyapunov functions to establish conditions for almost periodic solutions in distribution.

Contribution

It introduces new conditions involving Lyapunov functions that ensure the existence of almost periodic solutions in stochastic differential equations.

Findings

Established stability criteria using Lyapunov functions.

Proved existence of almost periodic solutions in distribution.

Linked stability properties with almost periodicity in stochastic systems.

Abstract

In this paper, we discuss the relationships between stability and almost periodicity for solutions of stochastic differential equations. Our essential idea is to get stability of solutions or systems by some inherited properties of Lyapunov functions. Under suitable conditions besides Lyapunov functions, we obtain the existence of almost periodic solutions in distribution.