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

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.