The semi-implicit Euler-Maruyama method for nonlinear non-autonomous stochastic differential equations driven by a class of L\'evy processes

TL;DR

This paper analyzes the strong convergence and invariant measure properties of a semi-implicit Euler-Maruyama method for nonlinear non-autonomous SDEs driven by Le9vy processes, revealing new dependence on process parameters.

Contribution

It introduces a novel analysis of convergence order dependence on Le9vy process parameters and studies the invariant measure convergence for the semi-implicit EM method.

Findings

Convergence order depends on Le9vy process parameters.

Existence and uniqueness of numerical invariant measure established.

Numerical examples confirm theoretical results.

Abstract

The strong convergence of the semi-implicit Euler-Maruyama (EM) method for stochastic differential equations with non-linear coefficients driven by a class of L\'evy processes is investigated. The dependence of the convergence order of the numerical scheme on the parameters of the class of L\'evy processes is discovered, which is different from existing results. In addition, the existence and uniqueness of numerical invariant measure of the semi-implicit EM method is studied and its convergence to the underlying invariant measure is also proved. Numerical examples are provided to confirm our theoretical results.