A CLASS OF STOCHASTIC FUNCTIONALDIFFERENTIAL EQUATIONSWITH MARKOVIAN SWITCHING

摘要

This paper investigates a class of stochas-tic functional differential equations with Markovian switch-ing. Under the local Lipschitz condition but not the lin-ear growth condition, this paper establishes existence-and-uniqueness theorems for the global solutions of these equa-tions. 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.