Strong convergence of the truncated Euler–Maruyama method for stochastic functional differential equations

Abstract

ABSTRACTIn this paper, we establish the truncated Euler–Maruyama (EM) method for stochastic functional differential equation (SFDE) and consider the strong convergence theory for the numerical solutions of SFDEs under the local Lipschitz condition plus Khasminskii-type condition instead of the linear growth condition. The type of convergence specifically addressed in this paper is strong- convergence for , and p is a parameter in Khasminskii-type condition. We also discussed the rates of -convergence for the truncated EM method.