Existence, Uniqueness And Asymptotic Properties of Neutrastochastic Functional Differential Equations with Markovian Switching

Abstract

This paper considers the existence and uniqueness of solution to neutral stochastic
functional differential equation with Markovian switching with local Lipschitz condition but
neither the linear growth condition. And we discuss the asymptotic properties of this solution
including moment boundedness and moment average boundedness in time. A One-dimension
nonlinear example is discussed to illustrate the theory.