非Lipschitz系数下随机泛函微分方程适度解的存在唯一性及其渐近性态(英文)  

Existence,Uniqueness and Asymptotic Behavior of Mild Solutions to Stochastic Functional Differential Equations With Non-Lipschitz Coefficients

作　　者：尹湘锋[1] 刘再明[2] 陈勇[1] 匡能晖[1] 

机构地区：[1]湖南科技大学数学与计算科学学院,湘潭湖南411201 [2]中南大学数学与计算技术学院,长沙湖南410075

出　　处：《数学进展》2012年第4期473-486,共14页Advances in Mathematics（China）

基　　金：supported by NSFC(No.10971230,No.11101137 and No.11126188);the Natural Science Foundation of Hunan Province(No.10JJ6014);the Research Foundation of Education Bureau of Hunan Province(No.11C0543)

摘　　要：本文主要运用Picard迭代和算子分数次幂方法,讨论了随机时滞偏微分方程适度解的存在性与唯一性,并对解的渐近性态进行了研究.这里方程的系数不满足Lipschitz条件,时滞r>0为有限的.最后给出了一个非Lipschitz条件的例子.In the present paper, sufficient conditions are given under which the existence and uniqueness of mild solutions to stochastic partial functional differential equations with finite delay r 〉 0 are obtained using a Picard type method of approximation and the semigroup method, where coefficients of the differential equations are non-Lipschitz. Moreover, the almost sure exponential stability of the mild solution is also studied. An example is given to illustrate our results.

关 键 词：随机泛函微分方程 时滞 Picard迭代 闭算子分数次幂 

分 类 号：O211.63[理学—概率论与数理统计]