The Truncated EM Method for Stochastic Differential Equations Driven by Fractional Brownian Motion

Abstract

We mainly focus on the numerical method of fractional Brownian motion in this paper. On the basis of the numerical method of general SDEs, an approximation scheme is obtained for the stochastic differential equations about fractional noise. And we get it by using the Lipschitz condition and combining with the truncation function f∆ and g∆. Furthermore, we also prove the moment boundedness and convergence of the solution by some lemma. At last, we apply this method to the Gilpin-Ayala model. The orbital image of the solution and the form of numerical solution are given. The error of solution also has been simulated by MATLAB.