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Maxima of continuous-time stationary stable processes

Part of: Stochastic processes Ergodic theory

Published online by Cambridge University Press:  01 July 2016

Gennady Samorodnitsky
Gennady Samorodnitsky*
Affiliation:
Cornell University
*
∗ Postal address: School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA. Email address: gennady@orie.cornell.edu
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Abstract

We study the suprema over compact time intervals of stationary locally bounded α-stable processes. The behaviour of these suprema as the length of the time interval increases turns out to depend significantly on the ergodic-theoretical properties of a flow generating the stationary process.

Keywords

Stable processstationary processergodic theorymaximaextreme value theorynon-singular flowdissipative flowconservative flowweak convergence

MSC classification

Primary: 60G10: Stationary processes 37A40: Nonsingular (and infinite-measure preserving) transformations
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 3 , September 2004 , pp. 805 - 823
Copyright
Copyright © Applied Probability Trust 2004 

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