Strong convergence of tamed $\theta$-EM scheme for neutral SDDEs with one-sided Lipschitz drift

TL;DR

This paper proves the strong convergence and convergence rates of a tamed $ heta$-EM scheme for neutral SDDEs with superlinear coefficients, applicable to equations driven by Brownian motion and jumps.

Contribution

It introduces a tamed $ heta$-EM scheme for neutral SDDEs with superlinear growth and establishes its strong convergence and rates, extending previous implicit scheme results.

Findings

Proves strong convergence of the scheme.

Establishes convergence rates for Brownian motion-driven equations.

Extends results to equations with jumps.

Abstract

This paper is concerned with strong convergence of a tamed $\theta$-Euler-Maruyama scheme for neutral stochastic differential delay equations with superlinearly growing coefficients. We not only prove the strong convergence of implicit schemes, but also reveal the convergence rate for these equations driven by Brownian motion and pure jumps, respectively.