Convergence of EM Scheme for Neutral Stochastic Differential Delay Equations

TL;DR

This paper investigates the convergence rates of the Euler-Maruyama scheme for neutral stochastic differential delay equations with polynomial growth terms, establishing a convergence rate of about one half for both Brownian-driven and jump process-driven cases.

Contribution

It provides the first analysis of EM scheme convergence rates for neutral SDDEs with polynomial growth, including both Brownian and jump process cases.

Findings

Convergence rate is approximately 0.5 for Brownian-driven SDDEs.

Convergence rate is close to 0.5 for jump process-driven SDDEs.

The results extend existing theory to more general SDDEs with polynomial growth.

Abstract

In this paper, we are concerned with convergence rate of Euler-Maruyama (EM) scheme for stochastic differential delay equations (SDDEs) of neutral type, where the neutral term, the drift term and the diffusion term are allowed to be of polynomial growth. More precisely, for SDDEs of neutral type driven by Brownian motions, we reveal that the convergence rate of the corresponding EM scheme is one half; Whereas for SDDEs of neutral type driven by jump processes, we show that the best convergence rate of the associated EM scheme is close to one half.