The Truncated Euler-Maruyama Method for Caputo Fractional Stochastic Differential Equations

In this paper, we firstly construct the truncated Euler-Maruyama (EM) method for Caputo fractional stochastic differential equations (Caputo FSDEs) with the local Lipschitz condition and the Khasminskii-type condition on drift and diffusion functions. After that, the boundedness and strong convergence of the numerical solutions are theoretically analyzed. Moreover, the strong convergence order of this presented truncated EM method is proved as alpha-0.5, where alpha denotes the order of Caputo derivative and 0.5<alpha<1. In the end, numerical experiments are demonstrated to confirm the correctness of the theoretical results.