Existence-uniqueness and continuation theorems for stochastic functional differential equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:245

Article

Xu, Daoyi¹  Yang, Zhiguo^1,2  Huang, Yumei¹ 

[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

关键词: stochastic functional differential equations;    existence;    uniqueness;    continuation theorem;   

DOI  :  10.1016/j.jde.2008.03.029

来源: Elsevier

【 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.

【 授权许可】

Free