A CLASS OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH MARKOVIAN SWITCHING

This paper investigates a class of stochastic functional differential equations with Markovian switching. Under the local Lipschitz condition but not the linear growth condition, this paper establishes existence-and-uniqueness theorems for the global solutions of these equations. This paper also examines asymptotic boundedness of the global solution, including boundedness in moment, stochastically ultimate boundedness and the moment average boundedness in time. To illustrate our idea more clearly, we consider a scalar stochastic polynomial equation and a special n-dimensional equation in detail.