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

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Type
Published Article
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Submission Date
Identifiers
DOI: 10.1214/009117904000000261
arXiv ID: math/0410149
Source
arXiv
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Unknown
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Abstract

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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