Numerical implementation of stochastic operational matrix driven by a fractional Brownian motion for solving a stochastic differential equation
Summary: An efficient method to determine a numerical solution of a stochastic differential equation (SDE) driven by fractional Brownian motion (FBM) with Hurst parameter \(H \in(1 / 2, 1)\) 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.
scientific article; zbMATH DE number 7022551
scientific article