Almost sure exponential stability for time-changed stochastic differential equations

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.