Existence and stability of almost periodic solutions to impulsive stochastic differential equations

Abstract

This paper introduces the concept of square-mean piecewise almost periodic for impulsive stochastic processes. The existence of square-mean piecewise almost periodic solutions for linear and nonlinear impulsive stochastic differential equations is established by using the theory of the semigroups of the operators and Schauder fixed point theorem. The stability of the square-mean piecewise almost periodic solutions for nonlinear impulsive stochastic differential equations is investigated.