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Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2003

Lengths and heights of random walk excursions

Abstract

Consider a simple symmetric random walk on the line. The parts of the random walk between consecutive returns to the origin are called excursions. The heights and lengths of these excursions can be arranged in decreasing order. In this paper we give the exact and limiting distributions of these ranked quantities. These results are analogues of the corresponding results of Pitman and Yor [1997, 1998, 2001] for Brownian motion.
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Dates and versions

hal-01183932 , version 1 (12-08-2015)

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Endre Csáki, Yueyun Hu. Lengths and heights of random walk excursions. Discrete Random Walks, DRW'03, 2003, Paris, France. pp.45-52, ⟨10.46298/dmtcs.3337⟩. ⟨hal-01183932⟩
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