Asymptotic exponential stability of modified truncated EM method for neutral stochastic differential delay equations

The aim of this paper is to investigate the asymptotic mean-square and almost sure exponential stability of modified truncated Euler-Maruyama method for neutral stochastic differential delay equations under non linear conditions. It is proved that the so called modified truncated Euler-Maruyama method is mean-square (almost surely) exponentially stable under suitable (local Lipschitz and Khasminskii-type) conditions. An example is provided to support our conclusions.