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

摘要

In this paper, we establish the truncated Euler-Maruyama (EM) method for stochastic functional differential equation (SFDE) dy(t) = f(y(t)) dt + g(y(t)) dB(t) 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-L-q convergence for 2 = q p, and p is a parameter in Khasminskii-type condition. We also discussed the rates of L-q-convergence for the truncated EM method.