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

TL;DR

This paper analyzes the strong convergence rates of a modified truncated Euler-Maruyama method applied to neutral stochastic differential delay equations, providing theoretical results under various conditions and illustrating them with examples.

Contribution

It establishes strong convergence rates for the modified truncated EM method for neutral stochastic delay equations under less restrictive conditions than usual.

Findings

Convergence rates are obtained under local Lipschitz and Khasminskii conditions.

Additional polynomial growth conditions yield convergence rates without weak monotonicity.

Two examples demonstrate the theoretical results.

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.