Stable stationary processes related to cyclic flows
Taqqu, Murad S.
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Citation (published version)V. Pipiras, M.S. Taqqu. 2004. "Stable stationary processes related to cyclic flows." ANNALS OF PROBABILITY, Volume 32, Issue 3A, pp. 2222 - 2260 (39). https://doi.org/10.1214/009117904000000108
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.