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Abstract and Applied Analysis
Volume 2014, Article ID 390418, 7 pages
http://dx.doi.org/10.1155/2014/390418
Research Article

Almost Sure and Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation

Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

Received 29 January 2014; Revised 24 May 2014; Accepted 24 May 2014; Published 4 June 2014

Academic Editor: Julio D. Rossi

Copyright © 2014 Qian Guo and Xueyin Tao. 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

The convergence of the split-step backward Euler (SSBE) method applied to stochastic differential equation with variable delay is proven in -sense. Almost sure convergence is derived from the convergence by Chebyshev’s inequality and the Borel-Cantelli lemma; meanwhile, the convergence rate is obtained.