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.

翻译：研究了一类Lévy过程驱动的非线性系数随机微分方程的半隐式Euler-Maruyama（EM）方法的强收敛性。发现了数值格式的收敛阶数对该类Lévy过程参数的依赖性，这一结果不同于现有文献。此外，研究了半隐式EM方法数值不变测度的存在唯一性，并证明了其向原系统不变测度的收敛性。数值算例验证了理论结果。