On a Class of Nonlocal Stochastic Functional Differential Equations with Infinite Delay

Abstract

This article considers a class of nonlocal stochastic functional differential equations with infinite delay whose coefficients are dependent the pth moment and establishes the existence-and-uniqueness theorem under the conditions that are similar to the classical linear growth condition and the Lipschitz condition. Compared with the existing results, the conditions of this article are easier to test.

Keywords:

• Existence and uniqueness
• Moment dependence
• Nonlocal stochastic functional differential equations

Mathematics Subject Classification:

• 60H10
• 34K50

Acknowledgments

The authors would like to thank the referees for their detailed comments and helpful suggestions. They also wish to thank the National Natural Science Foundation of China (Grant No. 11001091) and Chinese University Research Foundation (Grant No. 2010MS129) for their financial supports.