Stable stationary processes related to cyclic flows

Details Stable stationary processes related to cyclic flows Stable stationary processes related to cyclic flows

2004-10-05

arxiv.org/abs/math/0410114v1

Annals of Probability 2004, Vol. 32, No. 3A, 2222-2260

Mathematics

Probability

Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imsta

Scientific paper

10.1214/009117904000000108

We study stationary stable processes related to periodic and cyclic flows in the sense of Rosinski [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.

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