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

作　　者：徐燕[1] 李彩月 XU Yan;LI Caiyue(College of Mathematics and Information Science,Hebei University,Baoding 071002,China)

机构地区：[1]河北大学数学与信息科学学院,河北保定071002

出　　处：《河北大学学报（自然科学版）》2023年第1期9-15,共7页Journal of Hebei University(Natural Science Edition)

基　　金：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)。

摘　　要：利用分离-聚合的思想、泛函Ito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.By using the idea of nearly decomposability and aggregation,functional Ito 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.

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 

分 类 号：O211.63[理学—概率论与数理统计]