Fixed Point Theory and Applications 
Volume 2008 (2008), Article ID 407352, 11 pages
doi:10.1155/2008/407352
Research Article

Fixed Points and Stability in Neutral Stochastic Differential Equations with Variable Delays

Meng Wu,1 Nan-jing Huang,1 and Chang-Wen Zhao2

 1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2College of Business and Management, Sichuan University, Chengdu, Sichuan 610064, China
Received 4 April 2008; Accepted 9 June 2008

Recommended by Tomas Domínguez Benavides

Abstract

We consider the mean square asymptotic stability of a generalized linear neutral stochastic differential equation with variable delays by using the fixed point theory. An asymptotic mean square stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton, Zhang and Luo. Two examples are also given to illustrate our results.