Stable stationary processes related to cyclic flows

Vladas Pipiras ^[1] ; Murad S. Taqqu ^[1]
1. [1] Boston University
  
  Boston University
  
  City of Boston, Estados Unidos
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 32, Nº. 3, 1, 2004, págs. 2222-2260
Idioma: inglés
DOI: 10.1214/009117904000000108
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Resumen
- 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.