  In this paper, the stability behaviors of stochastic differential equations
(SDEs) driven by time-changed Brownian motions are discussed. Based on the
generalized Lyapunov method and stochastic analysis, necessary conditions are
provided for solutions of time-changed SDEs to be stable in differential
senses, such as stochastic stability, stochastically asymptotic stability and
globally stochastically asymptotic stability. Also, a connection between the
stability of the solution to the time-changed SDEs and that to their
corresponding non-time-changed SDEs is revealed by applying the duality
theorem. Finally, two examples are provided to illustrate the theoretical
results.
