Stochastic Operational Matrix Method for Solving Stochastic Differential Equation by a Fractional Brownian Motion

Abstract

This article proposes an effective method for solving stochastic differential equations (SDEs) driven by fractional Brownian motion with Hurst parameter \(H\in (0,{1\over 2})\) and n independent one-dimensional standard Brownian motion. Hat basis functions and their stochastic operational matrix, convert the SDE into a linear lower triangular system. Also, the error analysis of the proposed method is investigated and we prove that the order of convergence is \(O(h^2)\). Then, numerical examples affirm the efficiency of the method.