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.
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.
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