Frequently visited sites of the inner boundary of simple random walk range

研究成果: Contribution to journalArticle査読

1 被引用数 (Scopus)

抄録

This paper considers the question: how many times does a simple random walk revisit the most frequently visited site among the inner boundary points? It is known that in ℤ2, the number of visits to the most frequently visited site among all of the points of the random walk range up to time n is asymptotic to π-1(logn)2, while in ℤd(d≥3), it is of order log n. We prove that the corresponding number for the inner boundary is asymptotic to βdlogn for any d≥2, where βd is a certain constant having a simple probabilistic expression.

本文言語英語
ページ(範囲)1412-1432
ページ数21
ジャーナルStochastic Processes and their Applications
126
5
DOI
出版ステータス出版済み - 5 2016
外部発表はい

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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