关于一个循环随机漫步在t²上的局部时间

IF 0.4 Q4 STATISTICS & PROBABILITY

Theory of Probability and Mathematical Statistics Pub Date : 2021-12-07 DOI:10.1090/tpms/1156

V. Bohun, A. Marynych

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引用次数: 1

摘要

我们证明了Z 2 \mathbb {Z}^2上具有零均值和有限第二矩的平面随机行走到固定有限集合P∧Z 2p \子集\mathbb {Z}^2上的点的访问次数的泛函极限定理。这一证明是基于在到达间分布有缓慢变化尾的情况下，在更新时期伴有移民的随机过程的分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the local time of a recurrent random walk on ℤ²

We prove a functional limit theorem for the number of visits by a planar random walk on Z 2 \mathbb {Z}^2 with zero mean and finite second moment to the points of a fixed finite set P ⊂ Z 2 P\subset \mathbb {Z}^2 . The proof is based on the analysis of an accompanying random process with immigration at renewal epochs in case when the inter-arrival distribution has a slowly varying tail.

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来源期刊

Theory of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

CiteScore

1.30

自引率

0.00%

发文量