Abstract
This paper investigates the split-step theta (SST) method to approximate a class of time-changed stochastic differential equations, whose drift coefficient can grow super-linearly and diffusion coefficient obeys the global Lipschitz condition. The strong convergence of the SST method is proved, and the SST method attains the classical 1 of convergence. In addition, the mean square stability of the time-changed stochastic differential equations is investigated. Two examples are presented to show the consistency of the theoretical results.
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