The truncated Euler-Maruyama method for highly nonlinear neutral stochastic differential equations with time-dependent delay

Abstract

The main goal of this paper is to establish the $L^q$-convergence of the truncated Euler-Maruyama method for neutral stochastic differential equations with time-de\-pendent delay under the Khasminskii-type condition. Whole consideration is influenced by the presence of the neutral term and delay function. The main theoretical result is illustrated by an example. Since the main result is related to the $L^q$-convergence of the Euler-Maruyama method under the global Lipschitz condition on the coefficients of the equation under consideration, for completeness of the paper, the appropriate results are given in Appendix.