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

Abstract

This work investigates the strong and weak convergence orders of numerical methods for SDEs driven by time-changed Lévy noise under the globally Lipschitz conditions. Based on the duality theorem, we prove that the numerical approximation generated by the stochastic $\hat{I}¸$ method with $\hat{I}¸\in [0,1]$ 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.

27 pages, 18 figures