泊松过程驱动的双时间尺度多值随机微分方程的平均法

doi:10.3969/j.issn.1000-1565.2025.04.001

河北大学学报(自然科学版) ›› 2025, Vol. 45 ›› Issue (4): 337-342.DOI: 10.3969/j.issn.1000-1565.2025.04.001

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泊松过程驱动的双时间尺度多值随机微分方程的平均法

徐燕,高佩璇

收稿日期:2024-03-12 发布日期:2025-07-11
作者简介:徐燕(1985—),女,河北大学副教授,博士,主要从事动力系统与随机分析.E-mail:xuyan2008good@163.com
基金资助:
国家自然科学基金项目(11801128;12171135;11771115);河北省自然科学基金项目(A2018201109);河北大学引进高层次人才科研项目(801260201109)

Averaging principle for two-time-scale MSDEs driven by Poisson processes

XU Yan,GAO Peixuan

College of Mathematics and Information Science, Hebei University, Baoding 071002, China

Received:2024-03-12 Published:2025-07-11

摘要/Abstract

摘要： 针对一类由泊松过程驱动的多值随机微分方程,运用Itô公式与平均原理推导出对应的平均系统,并对其解进行定量比较.结果表明,在一定假设下,原系统的解在均方意义下收敛于平均系统的解.该结论不仅拓展了平均原理在随机系统中的应用范畴,也为多尺度随机动力系统的近似分析提供了新的理论工具.

关键词: 多值随机微分方程, 泊松过程, 随机平均法

Abstract: This paper focuses on a class of multi-valued stochastic differential equations(MSDEs)driven by Poisson processes. By applying Itôs formula and the averaging principle, the corresponding averaged system is derived, and a quantitative comparison of their solutions is conducted. The results show that, under certain assumptions, the solution of the original system converges to that of the averaged system in the mean-square sense. This conclusion not only expands the application scope of the averaging principle in stochastic systems but also provides a new theoretical tool for the approximate analysis of multi-scale stochastic dynamical systems.

Key words: MSDEs, Poisson processes, stochastic averaging principle

中图分类号:

O211.63

徐燕,高佩璇. 泊松过程驱动的双时间尺度多值随机微分方程的平均法[J]. 河北大学学报(自然科学版), 2025, 45(4): 337-342.

XU Yan,GAO Peixuan. Averaging principle for two-time-scale MSDEs driven by Poisson processes[J]. Journal of Hebei University(Natural Science Edition), 2025, 45(4): 337-342.

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泊松过程驱动的双时间尺度多值随机微分方程的平均法

Averaging principle for two-time-scale MSDEs driven by Poisson processes

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