Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes
Gennady Samorodnitsky
Source: Ann. Probab. Volume 32, Number 2 (2004), 1438-1468.
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.
Primary Subjects: 60G10, 37A40
Keywords: Stable process; stationary process; long memory; long range dependence; ergodic theory; maxima; extreme value theory; nonsingular flow; dissipative flow; conservative flow
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1084884857
Digital Object Identifier: doi:10.1214/009117904000000261
Mathematical Reviews number (MathSciNet):
MR2060304
Zentralblatt MATH identifier:
1049.60027
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