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July 2004 Stable stationary processes related to cyclic flows
Vladas Pipiras, Murad S. Taqqu
Ann. Probab. 32(3): 2222-2260 (July 2004). DOI: 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.


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Vladas Pipiras. Murad S. Taqqu. "Stable stationary processes related to cyclic flows." Ann. Probab. 32 (3) 2222 - 2260, July 2004.


Published: July 2004
First available in Project Euclid: 14 July 2004

zbMATH: 1054.60056
MathSciNet: MR2073190
Digital Object Identifier: 10.1214/009117904000000108

Primary: 60G10 , 60G52
Secondary: 37A40

Keywords: cocycles , Flows , Periodic and cyclic flows , Stable stationary processes

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 3 • July 2004
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