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

In this paper, we investigate the strong convergence of the semi-implicit Euler-Maruyama (EM) method for stochastic differential equations driven by a class of L\'evy processes. Comparing to existing results, we obtain the convergence order of the numerical scheme and discover its relation with the parameters of the class of L\'evy processes. 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.