具有无限时滞的随机泛函微分方程的解的唯一存在性(英文)

The Existence and Uniqueness of the Solution for Stochastic Functional Differential Equations with Infinite Delay at the Phase Space B

本文主要证明了在相空间B中具有无限时滞随机泛函微分方程解的唯一存在性.推广了文献[2]中的相空间,并且给出了一些相空间存在的例子.另外,本文建立了一个Ba-nach空间Mt20((-∞,T],Rd)依范数‖·‖,并在这个空间上讨论了具有无限时滞随机泛函微分方程的解的唯一存在性.

The main aim of this paper is to prove the existence and uniqueness of the solution forstochastic functional differential equations with infinite delay（short for ISFDEs）at phase space （B）.These extends phase space of the paper[2]and gives some examples to show that phase space （B） exits.Inaddition. This paper builds a Banach Space M^2t0（（-∞）,T],R^d）with norm‖·‖in order to discuss the existence and uniqueness of the solution for ISFDEs in it.