An Averaging Principle for Stochastic Differential Delay Equations Driven by Time-Changed Levy Noise

In this paper, we aim to derive an averaging principle for stochastic differential equations driven by time-changed Levy noise with variable delays. Under certain assumptions, we show that the solutions of stochastic differential equations with time-changed Levy noise can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence and in convergence in probability, respectively. The convergence order is also estimated in terms of noise intensity. Finally, an example with numerical simulation is given to illustrate the theoretical result.