Electronic Communications in Probability

Invariance Principles for Ranked Excursion Lengths and Heights

Endre Csaki and Yueyun Hu

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In this note we prove strong invariance principles between ranked excursion lengths and heights of a simple random walk and those of a standard Brownian motion. Some consequences concerning limiting distributions and strong limit theorems will also be presented.

Article information

Electron. Commun. Probab., Volume 9 (2004), paper no. 2, 14-21.

Accepted: 18 February 2004
First available in Project Euclid: 26 May 2016

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Zentralblatt MATH identifier

Primary: 60F17: Functional limit theorems; invariance principles 60F05: Central limit and other weak theorems 60F15: Strong theorems

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Csaki, Endre; Hu, Yueyun. Invariance Principles for Ranked Excursion Lengths and Heights. Electron. Commun. Probab. 9 (2004), paper no. 2, 14--21. doi:10.1214/ECP.v9-1103. https://projecteuclid.org/euclid.ecp/1464286682

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