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

doi:10.1007/s10473-022-0208-7

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (2): 540-550.doi: 10.1007/s10473-022-0208-7

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

申广君¹, 徐文涛¹, 吴奖伦²

1. Department of Mathematics, Anhui Normal University, Wuhu 241000, China;
2. Department of Mathematics, Computational Foundry Swansea University, Swansea, SA1 8EN, UK

收稿日期:2020-06-18 修回日期:2021-10-20 出版日期:2022-04-25 发布日期:2022-04-22
通讯作者: Jiang-Lun WU,E-mail:j.l.wu@swansea.ac.uk E-mail:j.l.wu@swansea.ac.uk
作者简介:Guangjun SHEN,E-mail:gjshen@163.com;Wentao XU,E-mail:wentaoxu1@163.com
基金资助:
This research is supported by the National Natural Science Foundation of China (12071003, 11901005) and the Natural Science Foundation of Anhui Province (2008085QA20).

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

Guangjun SHEN¹, Wentao XU¹, Jiang-Lun WU²

1. Department of Mathematics, Anhui Normal University, Wuhu 241000, China;
2. Department of Mathematics, Computational Foundry Swansea University, Swansea, SA1 8EN, UK

Received:2020-06-18 Revised:2021-10-20 Online:2022-04-25 Published:2022-04-22
Supported by:
This research is supported by the National Natural Science Foundation of China (12071003, 11901005) and the Natural Science Foundation of Anhui Province (2008085QA20).

摘要/Abstract

摘要： 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.

关键词: Averaging principle, stochastic differential equation, time-changed Lévy noise, variable delays

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

中图分类号:

34C29

申广君, 徐文涛, 吴奖伦. AN AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL DELAY EQUATIONS DRIVEN BY TIME-CHANGED LÉVY NOISE[J]. 数学物理学报(英文版), 2022, 42(2): 540-550.

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

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

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