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

Institut for Matematiske Fag

11 Citationer (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

Originalsprog	Engelsk
Tidsskrift	Bernoulli
Vol/bind	16
Udgave nummer	4
Sider (fra-til)	1016-1038
Antal sider	23
ISSN	1350-7265
DOI	https://doi.org/10.3150/10-BEJ255
Status	Udgivet - nov. 2010

Adgang til dokumentet

10.3150/10-BEJ255

Citationsformater

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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 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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N2 - 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

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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