Abstract and Applied Analysis

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

R. Ezzati, M. Khodabin, and Z. Sadati

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Abstract

An efficient method to determine a numerical solution of a stochastic differential equation (SDE) driven by fractional Brownian motion (FBM) with Hurst parameter H(1/2,1) and n 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 m equations and m unknowns. Then, the error analysis is demonstrated by some theorems and defnitions. Finally, the numerical examples demonstrate applicability and accuracy of this method.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 523163, 11 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412605903

Digital Object Identifier
doi:10.1155/2014/523163

Mathematical Reviews number (MathSciNet)
MR3182287

Zentralblatt MATH identifier
07022551

Citation

Ezzati, R.; Khodabin, M.; Sadati, Z. Numerical Implementation of Stochastic Operational Matrix Driven by a Fractional Brownian Motion for Solving a Stochastic Differential Equation. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 523163, 11 pages. doi:10.1155/2014/523163. https://projecteuclid.org/euclid.aaa/1412605903


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