Bernoulli

  • Bernoulli
  • Volume 16, Number 4 (2010), 1016-1038.

The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution

Thomas Mikosch and Alfredas Račkauskas

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Abstract

In this paper, we deal with the asymptotic distribution of the maximum increment of a random walk with a regularly varying jump size distribution. This problem is motivated by a long-standing problem on change point detection for epidemic alternatives. It turns out that the limit distribution of the maximum increment of the random walk is one of the classical extreme value distributions, the Fréchet distribution. We prove the results in the general framework of point processes and for jump sizes taking values in a separable Banach space.

Article information

Source
Bernoulli, Volume 16, Number 4 (2010), 1016-1038.

Dates
First available in Project Euclid: 18 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1290092894

Digital Object Identifier
doi:10.3150/10-BEJ255

Mathematical Reviews number (MathSciNet)
MR2759167

Zentralblatt MATH identifier
1215.60018

Keywords
Banach space valued random element epidemic change point extreme value theory Fréchet distribution maximum increment of a random walk point process convergence regular variation

Citation

Mikosch, Thomas; Račkauskas, Alfredas. The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution. Bernoulli 16 (2010), no. 4, 1016--1038. doi:10.3150/10-BEJ255. https://projecteuclid.org/euclid.bj/1290092894


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