Tamed EM scheme of Neutral Stochastic Differential Delay Equations

TL;DR

This paper studies the convergence properties of a tamed Euler-Maruyama scheme applied to neutral stochastic differential delay equations, providing strong convergence results and convergence rates under various conditions.

Contribution

It introduces and analyzes the tamed EM scheme for neutral stochastic delay equations, including convergence proofs and rate estimates under different assumptions.

Findings

Strong convergence under global and local conditions

Convergence rate is smaller than classical EM scheme rate

Applicable to a class of neutral stochastic delay equations

Abstract

In this paper, we investigate the convergence of the tamed Euler-Maruyama (EM) scheme for a class of neutral stochastic differential delay equations. The strong convergence results of the tamed EM scheme are presented under global and local non-Lipschitz conditions, respectively. Moreover, under a global Lipschitz condition, we provide the rate of the convergence of tamed EM, which is smaller than the rate convergence of classical EM scheme one half.