Strong convergence rates of modified truncated EM methods for neutral stochastic differential delay equations

Abstract

The aim of this paper is to investigate strong convergence of modified truncated Euler–Maruyama method for neutral stochastic differential delay equations introduced in Lan (2018). Strong convergence rates of the given numerical scheme to the exact solutions at fixed time T are obtained under local Lipschitz and Khasminskii-type conditions. Moreover, convergence rates over a time interval [0,T] are also obtained under additional polynomial growth condition on g without the weak monotonicity condition (which is usually the standard assumption to obtain the convergence rate). Two examples are presented to interpret our conclusions.