无限时滞的随机泛函微分方程解的渐近性质（英文）  

ASYMPTOTIC PROPERTIES OF A CLASS OF NONLINEAR STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

作　　者：王琳[1] 孙琳[1] 黄冬生[1] 温文豪 WANG Lin;SUN Lin;HUANG Dong-sheng;WEN Wen-hao(School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China)

机构地区：[1]广东工业大学应用数学学院,广东广州510520

出　　处：《数学杂志》2017年第4期769-780,共12页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11201083);Natural Science Foundation of Guangdong Province(S2013010016270);Foundation of College Students Innovation Project(XJ201511845094)

摘　　要：本文研究了无限时滞随机泛函微分方程解的存在唯一性,矩有界性的问题.利用Lyapunov函数法以及概率测度的引入得到了确保方程解在唯一、矩有界、时间平均矩有界同时成立的一个新的条件.推广了Khasminskii-Mao定理的相关结果.In this paper,the existence and uniqueness and moment boundedness of solutions to stochastic functional differential equations with innite delay are studied.By using the method of Lyapunov functions and the introduction of probability measures,a new condition which assures that the equations have a unique solution and at the same time the moment boundedness,the moment average in time boundedness of this solution is obtained.Relevant results about the Khasminskii-Mao theorems are generalized.

关 键 词：矩有界 伊藤公式 BROWN运动 无限时滞 

分 类 号：O211.63[理学—概率论与数理统计]