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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 565812, 11 pages
http://dx.doi.org/10.1155/2014/565812
Research Article

Numerical Schemes for Stochastic Differential Equations with Variable and Distributed Delays: The Interpolation Approach

Systems Engineering Institute, South China University of Technology, Guangzhou 510640, China

Received 10 October 2013; Accepted 30 December 2013; Published 24 February 2014

Academic Editor: Patricia J. Y. Wong

Copyright © 2014 Xueyan Zhao et al. 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

A kind of the Euler-Maruyama schemes in discrete forms for stochastic differential equations with variable and distributed delays is proposed. The linear interpolation method is applied to deal with the values of the solutions at the delayed instants. The assumptions of this paper on the coefficients and related parameters are somehow weaker than those imposed by the related past literature. The error estimations for the Euler-Maruyama schemes are given, which are proved to be the same as those for the fundamental Euler-Maruyama schemes.