Abstract

This paper introduces a numerical method for solving the nonlinear stochastic differential equations (NSDEs) driven by  independent one-dimensional fractional Brownian motion with hurst parameters  The method is stated by conversion of the fractional Brownian motion to the standard Brownian motion combined with the collocation method. Using this approach, the NSDEs are reduced to a stochastic nonlinear system of   equations and  unknowns. Finally, error analysis is given on some theorems and assumptions on the coefficients of the NSDEs. Also, applicability and accuracy of method is stated by a numerical example in field of a stochastic population growth model.

Keywords

Block pulse functions; Fractional Brownian motion; Standard Brownian motion; Collocation method; Nonlinear stochastic differential equations

Introduction