Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes

2004/04/01 by Gennady Samorodnitsky
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chaos control and synchronization #math.PR #msc:37A40 #msc:60G10 #stochastic dynamics and bifurcation

paper · pdf · doi:10.1214/009117904000000261

published as Annals of Probability 2004, Vol. 32, No. 2, 1438-1468 · Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000261

openalex publication_date 2004/04/01 · arxiv created 2004/10/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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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