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

Thomas Valentin Mikosch; Alfredas Rackauskas

doi:10.3150/10-BEJ255

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

Thomas Valentin Mikosch, Alfredas Rackauskas

Department of Mathematical Sciences

11 Citations (Scopus)

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

Original language	English
Journal	Bernoulli
Volume	16
Issue number	4
Pages (from-to)	1016-1038
Number of pages	23
ISSN	1350-7265
DOIs	https://doi.org/10.3150/10-BEJ255
Publication status	Published - Nov 2010

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10.3150/10-BEJ255

Cite this

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title = "The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution",

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 Fr{\'e}chet distribution. We prove the results in the general framework of point processes and for jump sizes taking values in a separable Banach space",

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AB - 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

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