Strong convergence rate of the truncated Euler-Maruyama method for stochastic differential delay equations with Poisson jumps

TL;DR

This paper analyzes the strong convergence rate of the truncated Euler-Maruyama method applied to stochastic differential delay equations with Poisson jumps, providing theoretical insights into numerical solution accuracy.

Contribution

It establishes the convergence and rate of the truncated Euler-Maruyama method for SDDEs with Poisson jumps under generalized Khasminskii conditions.

Findings

Proved strong convergence of the numerical method.

Derived explicit convergence rate.

Validated theoretical results with simulations.

Abstract

In this paper, we study a class of super-linear stochastic differential delay equations with Poisson jumps (SDDEwPJs). The convergence and rate of the convergence of the truncated Euler-Maruyama numerical solutions to SDDEwPJs are investigated under the generalized Khasminskii-type condition.