AN AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL DELAY EQUATIONS DRIVEN BY TIME-CHANGED LÉVY NOISE

doi:10.1007/s10473-022-0208-7

Abstract

Abstract: In this paper, we aim to derive an averaging principle for stochastic differential equations driven by time-changed Lévy noise with variable delays. Under certain assumptions, we show that the solutions of stochastic differential equations with time-changed Lévy 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.

Key words: Averaging principle, stochastic differential equation, time-changed Lévy noise, variable delays

CLC Number:

34C29

Guangjun SHEN, Wentao XU, Jiang-Lun WU. AN AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL DELAY EQUATIONS DRIVEN BY TIME-CHANGED LÉVY NOISE[J].Acta mathematica scientia,Series B, 2022, 42(2): 540-550.

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