{"title":"On the local time of a recurrent random walk on ℤ²","authors":"V. Bohun, A. Marynych","doi":"10.1090/tpms/1156","DOIUrl":null,"url":null,"abstract":"We prove a functional limit theorem for the number of visits by a planar random walk on \n\n \n \n \n Z\n \n 2\n \n \\mathbb {Z}^2\n \n\n with zero mean and finite second moment to the points of a fixed finite set \n\n \n \n P\n ⊂\n \n \n Z\n \n 2\n \n \n P\\subset \\mathbb {Z}^2\n \n\n. 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.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2021-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and Mathematical Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tpms/1156","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
Abstract
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.