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

Gennady Samorodnitsky
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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. 2004-10-06. Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes. https://doi.org/10.1214/009117904000000261

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