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

Abstract EN

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.