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November 2010 The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution
Thomas Mikosch, Alfredas Račkauskas
Bernoulli 16(4): 1016-1038 (November 2010). DOI: 10.3150/10-BEJ255

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.

Citation

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Thomas Mikosch. Alfredas Račkauskas. "The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution." Bernoulli 16 (4) 1016 - 1038, November 2010. https://doi.org/10.3150/10-BEJ255

Information

Published: November 2010
First available in Project Euclid: 18 November 2010

zbMATH: 1215.60018
MathSciNet: MR2759167
Digital Object Identifier: 10.3150/10-BEJ255

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

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability

Vol.16 • No. 4 • November 2010
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