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

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 oper...

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Published in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.153-163-816
Main Authors: Ezzati, R., Sadati, Z., Khodabin, M.
Format: Article
Language:English
Subjects:
Brownian motion
Confidence intervals
Mathematical research
Matrices
Numerical analysis
Standard deviation
Stochastic differential equations
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description 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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subjects Brownian motion
Confidence intervals
Mathematical research
Matrices
Numerical analysis
Standard deviation
Stochastic differential equations
title Numerical Implementation of Stochastic Operational Matrix Driven by a Fractional Brownian Motion for Solving a Stochastic Differential Equation
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