Abstract and Applied Analysis
Volume 2011 (2011), Article ID 143079, 14 pages
http://dx.doi.org/10.1155/2011/143079
Research Article

Almost Surely Asymptotic Stability of Exact and Numerical Solutions for Neutral Stochastic Pantograph Equations

Zhanhua Yu

Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China

Received 26 March 2011; Revised 29 June 2011; Accepted 29 June 2011

Academic Editor: Nobuyuki Kenmochi

Copyright © 2011 Zhanhua Yu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the almost surely asymptotic stability of exact solutions to neutral stochastic pantograph equations (NSPEs), and sufficient conditions are obtained. Based on these sufficient conditions, we show that the backward Euler method (BEM) with variable stepsize can preserve the almost surely asymptotic stability. Numerical examples are demonstrated for illustration.