Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

, Volume 68, Issue 3, pp 365–382

On the length of the longest excursion

  • E. Csáki
  • P. Erdős
  • P. Révész
Article

DOI: 10.1007/BF00532646

Cite this article as:
Csáki, E., Erdős, P. & Révész, P. Z. Wahrscheinlichkeitstheorie verw Gebiete (1985) 68: 365. doi:10.1007/BF00532646

Summary

A lower limit of the length of the longest excursion of a symmetric random walk is given. Certain related problems are also discussed. It is shown e.g. that for any ɛ>0 and all sufficiently large n there are c(ɛ) loglog n excursions in the interval (0, n) with total length greater than n(1−ɛ), with probability 1.

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • E. Csáki
    • 1
  • P. Erdős
    • 1
  • P. Révész
    • 1
  1. 1.Mathematical InstituteBudapestHungary