循环随机漫步上的函数

Pub Date : 2023-03-01 DOI:10.35634/vm230108

V.R. Manivannan, M. Venkataraman

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引用次数: 0

摘要

如果在可数无限状态空间上的随机行走是可逆的，则存在已知的循环行走的充分必要条件。当可逆性条件被丢弃时，通过使用离散狄利克雷解和平衡(势理论中熟悉的概念)，可以部分地恢复上述关于随机漫步的递归性和暂态性的一些结果。

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Delta-functions on recurrent random walks

If a random walk on a countable infinite state space is reversible, there are known necessary and sufficient conditions for the walk to be recurrent. When the condition of reversibility is dropped, by using discrete Dirichlet solutions and balayage (concepts familiar in potential theory) one could partially retrieve some of the above results concerning the recurrence and the transience of the random walk.

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