Mean square stability of the split-step theta method for non-linear time-changed stochastic differential equations

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.

Keywords:

• Time-changed stochastic differential equations
• split-step theta method
• strong convergence
• mean square stability

AMS SUBJECT CLASSIFICATIONS:

• 60H10
• 65C30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China [11901058] Natural Science Foundation of Hubei Province [2021CFB543].