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

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

2010-11-26

arxiv.org/abs/1011.5718v1

Bernoulli 2010, Vol. 16, No. 4, 1016-1038

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ255 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ255

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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