The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:331

Article

Wei Fengying ; Wang Ke

关键词: Stochastic functional differential equations;    infinite delay;    existence;    uniqueness;   

DOI  :  10.1016/j.jmaa.2006.09.020

来源: Elsevier

【 摘 要 】

This paper is devoted to build the existence-and-uniqueness theorem of solutions to stochastic functional differential equations with infinite delay (short for ISFDEs) at phase space BC((-infinity, 0]; R-d). Under the uniform Lipschitz condition, the linear growth condition is weaked to obtain the moment estimate of the solution for ISFDEs. Furthermore, the existence-and-uniqueness theorem of the solution for ISFDEs is derived, and the estimate for the error between approximate solution and accurate solution is given. On the other hand, under the linear growth condition, the uniform Lipschitz condition is replaced by the local Lipschitz condition, the existence-and-uniqueness theorem is also valid for ISFDEs on [t(0), T]. Moreover, the existence-and-uniqueness theorem still holds on interval [t(0), infinity), where t(0) is an element of R is an arbitrary real number. (C) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free