Existence-uniqueness and continuation theorems for stochastic functional differential equations

被引：49

作者：

Xu, Daoyi ^{[1
]}

Yang, Zhiguo ^{[1
,2
]}

Huang, Yumei ^{[1
]}

机构：

[1] Sichuan Univ, Yangtze Ctr Math, Chengdu 610064, Peoples R China

[2] Sichuan Normal Univ, Coll Math & Software Sci, Chengdu 610066, Sichuan, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2008年 / 245卷 / 06期

基金：

中国国家自然科学基金;

关键词：

stochastic functional differential equations; existence; uniqueness; continuation theorem;

D O I：

10.1016/j.jde.2008.03.029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main aim of this paper is to develop some basic theories of stochastic functional differential equations (SFDEs). Firstly, we establish stochastic versions of the well-known Picard local existence-uniqueness theorem given by Driver and continuation theorems given by Hale and Driver for functional differential equations (FDEs). Then, we extend the global existence-uniqueness theorems of Wintner for ordinary differential equations (ODEs), Driver for FDEs and Taniguchi for stochastic ordinary differential equations (SODEs) to SFDEs. These show clearly the power of our new results. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：1681 / 1703

页数：23

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