Tamed EM schemes for neutral stochastic differential delay equations with superlinear diffusion coefficients

Abstract

In this article, we propose two types of explicit tamed Euler–Maruyama (EM) schemes for neutral stochastic differential delay equations with superlinearly growing drift and diffusion coefficients. The first type is convergent in the Lq sense under the local Lipschitz plus Khasminskii-type conditions. The second type is of order half in the mean-square sense under the Khasminskii-type, global monotonicity and polynomial growth conditions. Moreover, it is proved that the partially tamed EM scheme has the property of mean-square exponential stability. Numerical examples are provided to illustrate the theoretical findings.