Existence and exponential stability of almost automorphic mild solutions for stochastic functional differential equations

Abstract

Abstract In this paper, the concept of p-mean almost automorphy for stochastic processes is firstly introduced. Some properties of the p-mean almost automorphic stochastic processes are further studied. Based on these properties, a class of stochastic functional differential equations given by is investigated. Under suitable assumptions, the existence, uniqueness and exponential stability of quadratic-mean almost automorphic mild solutions for the equations are discussed by means of semigroups of operators and by Banach contraction principle. Moreover, the quadratic-mean almost automorphic mild solutions for semilinear stochastic partial functional differential equations, which is illustrated by example, are in good agreement with the theoretical analysis. Keywords: existence and uniquenessquadratic-mean almost automorphic solutionstochastic functional differential equationsexponential stabilityBanach contraction principle Acknowledgement This work is supported by the National Natural Science Foundation of China (No. 10871074). Notes 1. Email: jfcaomath@163.com 2. Email: zaitanghuang@163.com Additional informationNotes on contributorsJunfei Cao 1 Zaitang Huang 2