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.
Publié le : 2004-04-14
Classification:
Stable process,
stationary process,
long memory,
long range dependence,
ergodic theory,
maxima,
extreme value theory,
nonsingular flow,
dissipative flow,
conservative flow,
60G10,
37A40
@article{1084884857,
author = {Samorodnitsky, Gennady},
title = {Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes},
journal = {Ann. Probab.},
volume = {32},
number = {1A},
year = {2004},
pages = { 1438-1468},
language = {en},
url = {http://dml.mathdoc.fr/item/1084884857}
}
Samorodnitsky, Gennady. Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes. Ann. Probab., Tome 32 (2004) no. 1A, pp. 1438-1468. http://gdmltest.u-ga.fr/item/1084884857/