A Multi-level Monte Carlo simulation for invariant distribution of Markovian switching L\'evy-driven SDEs with super-linearly growth coefficients

TL;DR

This paper introduces a novel numerical scheme combining tamed-adaptive Euler-Maruyama and Multi-level Monte Carlo methods to approximate the invariant distribution of Markovian switching Lévy-driven SDEs with super-linear coefficients.

Contribution

It develops a new approximation scheme capable of handling super-linear growth in coefficients for Markovian switching Lévy-driven SDEs.

Findings

Effective approximation of invariant distributions achieved.

Applicable to SDEs with super-linear growth coefficients.

Enhanced computational efficiency through multi-level Monte Carlo.

Abstract

This paper concerns the numerical approximation for the invariant distribution of Markovian switching L\'evy-driven stochastic differential equations. By combining the tamed-adaptive Euler-Maruyama scheme with the Multi-level Monte Carlo method, we propose an approximation scheme that can be applied to stochastic differential equations with super-linear growth drift and diffusion coefficients.