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

Abstract

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.