标题：Existence, uniqueness and stability of the solution to neutral stochastic functional differential equations with infinite delay under non-Lipschitz conditions
摘要：Choosing space C g as the phase space, the existence, uniqueness and stability of the solution to neutral stochastic functional differential equations with infinite delay (short for INSFDEs) are studied in this paper. Under non-Lipschitz condition, weakened linear growth condition and contractive condition, the existence-and-uniqueness theorem of the solution to INSFDEs by means of the Picard iteration, Doob’s martingale inequalities, Gronwall’s inequality and Bihari’s inequality is obtained. Furthermore, the continuous dependence of the solutions on the initial value to INSFDEs are derived. MSC:65C30, 60H10.
关键词：neutral stochastic functional differential equations ; infinite delay ; phase space C g ; non-Lipschitz condition ; existence-and-uniqueness theorem ; stability
