标题： 时间变化Lévy噪声驱动的SDE数值方法的强弱收敛阶 显示英文标题

标题： Strong and weak convergence orders of numerical methods for SDEs driven by time-changed Lévy noise

摘要： 本文研究了在全局Lipschitz条件下，由时间变换的Lévy噪声驱动的随机微分方程数值方法的强收敛阶和弱收敛阶。基于对偶定理，我们证明了由随机 $\theta$ 方法生成的数值逼近与反向子ordinator的模拟，在 $\theta \in [0,1]$ 条件下强收敛，收敛阶为 $1/2$。此外，通过Kolmogorov向后偏积分-微分方程，结合Euler-Maruyama方法和反向子ordinator估计的数值逼近被证明具有弱收敛阶 $1$。最后，这些理论结果通过一些数值实验得到了验证。 显示英文摘要

摘要： This work investigates the strong and weak convergence orders of numerical methods for SDEs driven by time-changed L\'{e}vy noise under the globally Lipschitz conditions. Based on the duality theorem, we prove that the numerical approximation generated by the stochastic $\theta$ method with $\theta \in [0,1]$ and the simulation of inverse subordinator converges strongly with order $1/2$. Moreover, the numerical approximation combined with the Euler--Maruyama method and the estimate of inverse subordinator is shown to have the weak convergence order $1$ by means of the Kolmogorov backward partial integro differential equations. These theoretical results are finally confirmed by some numerical experiments.