Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:220

Article

Ren, Yong¹  Lu, Shiping¹  Xia, Ningmao² 

[1] Anhui Normal Univ, Dept Math, Wuhu 241000, Peoples R China

[2] E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

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

DOI  :  10.1016/j.cam.2007.08.022

来源: Elsevier

【 摘 要 】

In this paper, we obtain some results on the existence and uniqueness of solutions to stochastic functional differential equations with infinite delay at phase space BC((-infinity. 0 vertical bar; R-d) which denotes the family of bounded continuous R-d-value functions phi defined on (-infinity. 0 vertical bar with norm parallel to phi parallel to = sup(-infinity < 0 <= 0) vertical bar phi (0)vertical bar under non-Lipschitz condition with Lipschitz condition being considered as a special case and a weakened linear growth condition. The solution is constructed by the successive approximation. (c) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free