KHASMINSKII-TYPE THEOREMS FOR STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

被引：23

作者：

Song, Minghui ^{[1
]}

Hu, Liangjian ^{[2
]}

Mao, Xuerong ^{[3
]}

Zhang, Liguo ^{[4
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

[2] Donghua Univ, Dept Appl Math, Shanghai 201600, Peoples R China

[3] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland

[4] Beijing Univ Technol, Sch Elect Informat & Control Engn, Beijing 100124, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2013年 / 18卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Brownian motion; Ito's formula; Khasminskii-test; Khasminskii-type condition; stochastic functional differential equations;

D O I：

10.3934/dcdsb.2013.18.1697

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a stochastic functional differential equation (SFDE) to have a unique global solutionit is in general required that the coefficients of the SFDE obey the local Lipschitz condition and the linear growth condition. However, there are many SFDEs in practice which do not obey the linear growth condition.The main aim of this paper is to establish existence-and-uniqueness theorems for SFDEs where the linear growth conditionis replaced by more general Khasminskii-type conditions in terms of a pair of Laypunov-type function.

引用

页码：1697 / 1714

页数：18

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