Large favourite sites of simple random walk and the wiener process

E. Csáki, Zhan Shi

Research output: Contribution to journalArticle

1 Citation (Scopus)


Let U(n) denote the most visited point by a simple symmetric random walk (Sk)k≥0 in the first n steps. It is known that U(n) and max0 ≤ xk ≤ n Sk satisfy the same law of the iterated logarithm, but have different upper functions (in the sense of P. Lévy). The distance between them however turns out to be transient. In this paper, we establish the exact rate of escape of this distance. The corresponding problem for the Wiener process is also studied.

Original languageEnglish
Pages (from-to)1-31
Number of pages31
JournalElectronic Journal of Probability
Publication statusPublished - Jan 1 1998



  • Favourite site
  • Local time
  • Random walk
  • Wiener process

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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