论文标题
非线性非自治的随机微分方程的半漆欧拉山方法由一类Lévy过程驱动
The semi-implicit Euler-Maruyama method for nonlinear non-autonomous stochastic differential equations driven by a class of Lévy processes
论文作者
论文摘要
研究了由一类Lévy过程驱动的非线性系数的半平均Euler-Maruyama（EM）方法的强烈收敛。发现数值方案的收敛顺序对莱维过程类别的参数的依赖性被发现，这与现有结果不同。此外，还研究了半密码EM方法的数值不变度度量的存在和唯一性，并证明了其与基本不变度度量的收敛性。提供数值示例以确认我们的理论结果。
The strong convergence of the semi-implicit Euler-Maruyama (EM) method for stochastic differential equations with non-linear 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 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.
