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

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

2004-10-06

arxiv.org/abs/math/0410149v1

Annals of Probability 2004, Vol. 32, No. 2, 1438-1468

Mathematics

Probability

Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imsta

Scientific paper

10.1214/009117904000000261

We study the partial maxima of stationary \alpha-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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