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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 523163, 11 pages
http://dx.doi.org/10.1155/2014/523163
Research Article

Numerical Implementation of Stochastic Operational Matrix Driven by a Fractional Brownian Motion for Solving a Stochastic Differential Equation

Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

Received 16 November 2013; Revised 20 January 2014; Accepted 20 January 2014; Published 11 March 2014

Academic Editor: Hamid Reza Karimi

Copyright © 2014 R. Ezzati 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

An efficient method to determine a numerical solution of a stochastic differential equation (SDE) driven by fractional Brownian motion (FBM) with Hurst parameter and independent one-dimensional standard Brownian motion (SBM) is proposed. The method is stated via a stochastic operational matrix based on the block pulse functions (BPFs). With using this approach, the SDE is reduced to a stochastic linear system of equations and unknowns. Then, the error analysis is demonstrated by some theorems and defnitions. Finally, the numerical examples demonstrate applicability and accuracy of this method.