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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 157498, 9 pages
http://dx.doi.org/10.1155/2014/157498
Research Article

Strong Convergence of the Split-Step Theta Method for Stochastic Delay Differential Equations with Nonglobally Lipschitz Continuous Coefficients

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

Received 27 April 2014; Accepted 6 August 2014; Published 20 August 2014

Academic Editor: Jaeyoung Chung

Copyright © 2014 Chao Yue and Chengming Huang. 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

This paper is concerned with the convergence analysis of numerical methods for stochastic delay differential equations. We consider the split-step theta method for nonlinear nonautonomous equations and prove the strong convergence of the numerical solution under a local Lipschitz condition and a coupled condition on the drift and diffusion coefficients. In particular, these conditions admit that the diffusion coefficient is highly nonlinear. Furthermore, the obtained results are supported by numerical experiments.