Almost sure exponential stability for time-changed stochastic differential equations

Volume 10, Issue 11, pp 5985--5998 http://dx.doi.org/10.22436/jnsa.010.11.35

Publication Date: November 24, 2017 Submission Date: January 10, 2017

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Authors

Yongxiang Zhu - College of Traffic Engineering, Hunan University of Technology, Zhuzhou, Hunan, 412007, China. Min Zhu - College of Traffic Engineering, Hunan University of Technology, Zhuzhou, Hunan, 412007, China. - School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, China. Junping Li - School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, China.

Abstract

Some sufficient conditions for almost sure exponential stability of solutions to time-changed stochastic differential equations (SDEs) are presented. The principle technique of our investigation is to construct a proper Lyapunov function and carry out generalized Lyapunov methods to time-changed SDEs. In contrast to the almost sure exponential stability in existing articles, we present new results on the stability of solutions to time-changed SDEs. Finally, an example is given to demonstrate the effectiveness of our work.

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Keywords

• Time-changed stochastic differential equations
• almost sure exponential stability
• time-changed Brownian motion

MSC

•  60H20
•  60H30

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