Stability of stochastic differential equations driven by the time-changed Lévy process with impulsive effects

Abstract

The stability of nonlinear stochastic differential equations driven by time-changed Lévy process with impulsive effects is discussed in this paper. Some sufficient conditions are provided to guarantee the solutions to be stable in different senses. The stochastic perturbation is also investigated for some unstable time-changed differential equations with impulses. The efficiency of the proposed results is illustrated by some examples with numerical simulations.