We study stationary stable processes related to periodic and cyclic flows in the sense of Rosiński [Ann. Probab. 23 (1995) 1163–1187]. These processes are not ergodic. We provide their canonical representations, consider examples and show how to identify them among general stationary stable processes. We conclude with the unique decomposition in distribution of stationary stable processes into the sum of four major independent components: 1. A mixed moving average component. 2. A harmonizable (or “trivial”) component. 3. A cyclic component 4. A component which is different from these.
Publié le : 2004-07-14
Classification:
Stable stationary processes,
flows,
periodic and cyclic flows,
cocycles,
60G52,
60G10,
37A40
@article{1089808424,
author = {Pipiras, Vladas and Taqqu, Murad S.},
title = {Stable stationary processes related to cyclic flows},
journal = {Ann. Probab.},
volume = {32},
number = {1A},
year = {2004},
pages = { 2222-2260},
language = {en},
url = {http://dml.mathdoc.fr/item/1089808424}
}
Pipiras, Vladas; Taqqu, Murad S. Stable stationary processes related to cyclic flows. Ann. Probab., Tome 32 (2004) no. 1A, pp. 2222-2260. http://gdmltest.u-ga.fr/item/1089808424/