The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution
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The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution. / Mikosch, Thomas Valentin; Rackauskas, Alfredas.
In: Bernoulli, Vol. 16, No. 4, 2010, p. 1016-1038.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - The limit distribution of the maximum increment of a random walk with regularly varying jump size distribution
AU - Mikosch, Thomas Valentin
AU - Rackauskas, Alfredas
PY - 2010
Y1 - 2010
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
U2 - 10.3150/10-BEJ255
DO - 10.3150/10-BEJ255
M3 - Journal article
VL - 16
SP - 1016
EP - 1038
JO - Bernoulli
JF - Bernoulli
SN - 1350-7265
IS - 4
ER -
ID: 33967632