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April 2004 Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes
Gennady Samorodnitsky
Ann. Probab. 32(2): 1438-1468 (April 2004). DOI: 10.1214/009117904000000261

Abstract

We study the partial maxima of stationary α-stable processes. We relate their asymptotic behavior to the ergodic theoretical properties of the flow. We observe a sharp change in the asymptotic behavior of the sequence of partial maxima as flow changes from being dissipative to being conservative, and argue that this may indicate a change from a short memory process to a long memory process.

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Gennady Samorodnitsky. "Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes." Ann. Probab. 32 (2) 1438 - 1468, April 2004. https://doi.org/10.1214/009117904000000261

Information

Published: April 2004
First available in Project Euclid: 18 May 2004

zbMATH: 1049.60027
MathSciNet: MR2060304
Digital Object Identifier: 10.1214/009117904000000261

Subjects:
Primary: 37A40 , 60G10

Keywords: conservative flow , dissipative flow , ergodic theory , Extreme value theory , long memory , Long range dependence , Maxima , nonsingular flow , Stable process , stationary process

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 2 • April 2004
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