The most visited site of Brownian motion and simple random walk

Richard F. Bass, Philip S. Griffin

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


Let L(t, x) be the local time at x for Brownian motion and for each t, let {Mathematical expression}, the absolute value of the most visited site for Brownian motion up to time t. In this paper we prove that -V(t) is transient and obtain upper and lower bounds for the rate of growth of -V(t). The main tools used are the Ray-Knight theorems and William's path decomposition of a diffusion. An invariance principle is used to get analogous results for simple random walks. We also obtain a law of the iterated logarithm for -V(t).

Original languageEnglish (US)
Pages (from-to)417-436
Number of pages20
JournalZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Issue number3
StatePublished - Sep 1985
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • General Mathematics


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