The strong convergence of the semi-implicit Euler–Maruyama (EM) method for stochastic differential equations with nonlinear coefficients driven by a class of Lévy processes is investigated. The dependence of the convergence order of the numerical scheme on the parameters of the class of Lévy processes is discovered, which is different from existing results. In addition, the existence and uniqueness of the numerical invariant measure for 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.
Li et al. (Wed,) studied this question.