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

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  • R. Ezzati
  • M. Khodabin
  • Z. Sadati

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.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:523163
DOI: 10.1155/2014/523163
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