On the length of the longest excursion
- Cite this article as:
- Csáki, E., Erdős, P. & Révész, P. Z. Wahrscheinlichkeitstheorie verw Gebiete (1985) 68: 365. doi:10.1007/BF00532646
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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.