Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay

摘要

In this paper, we obtain the existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay at phase space ВС((_oo,0];R~d) which denotes the family of bounded continuous R~d- value functions q defined on (_co, 0] withnorm Ilψll = sup_-_Iψ(_) under non-Lipschitz condition with Lipschitz condition being considered as a special case and a weakened linear growth condition. The solution is con_structed by the successive approximation. Furthermore, we give the continuous depen_dence of solutions on the initial value by means of the Corollary of Binary inequality.