具有随机切换的泛函Liénard方程的平均法

doi:10.3969/j.issn.1000-1565.2023.01.002

河北大学学报(自然科学版) ›› 2023, Vol. 43 ›› Issue (1): 9-15.DOI: 10.3969/j.issn.1000-1565.2023.01.002

具有随机切换的泛函Liénard方程的平均法

徐燕,李彩月

收稿日期:2022-01-19 出版日期:2023-01-25 发布日期:2023-02-22
作者简介:徐燕(1985—),女,安徽潜山人,河北大学副教授,博士,主要从事动力系统与随机分析研究.
E-mail:xuyan2008good@163.com
基金资助:
国家自然科学基金资助项目(11801128;11771115);河北省自然科学基金资助项目(A2018201109);河北大学引进高层次人才科研项目(801260201109)

Averaging principle for stochastic function Liénard equations with random switching

XU Yan, LI Caiyue

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

Received:2022-01-19 Online:2023-01-25 Published:2023-02-22

摘要/Abstract

摘要： 利用分离-聚合的思想、泛函Itô公式和平均法,研究具有随机切换的泛函Liénard方程的平均法.由于此系统 Markov链所处的状态空间很大且具有泛函项,直接处理原系统是非常复杂的.在一定条件下, 证明原系统收敛到一个极限过程,此极限过程相较于原系统更利于计算和分析,进而通过研究极限过程得到原系统的性质.

关键词: 随机切换, 随机平均法, 鞅问题公式, 随机泛函微分方程

Abstract: By using the idea of nearly decomposability and aggregation, functional Itô formula and the averaging principle, this article considers the averaging principle for the stochastic functional Liénard equations with random switching was considered. Because the Markov chain is in a large state space and involves functional diffusions, the original system was dealt with. Under suitable conditions, it shows that the original system converges to a limit process, which is more convenient for calculation and analysis. The properties of the original system are obtained by studying the limiting process.

Key words: random switching, averaging principle, martingale problem formulation, stochastic functional differential equations

中图分类号:

O211.63

徐燕,李彩月. 具有随机切换的泛函Liénard方程的平均法[J]. 河北大学学报(自然科学版), 2023, 43(1): 9-15.

XU Yan, LI Caiyue. Averaging principle for stochastic function Liénard equations with random switching[J]. Journal of Hebei University(Natural Science Edition), 2023, 43(1): 9-15.

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具有随机切换的泛函Liénard方程的平均法

Averaging principle for stochastic function Liénard equations with random switching

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