Summary
We show that symmetric α-stable moving average processes are not harmonizable. However, we show that a concept of generalized spectrum holds for allL p -bounded processes O<p<-2. In capep=2, generalized spectrum is a measure and the classical representation follows. For strongly harmonizable symmetric α-stable processes we derive necessary and sufficient conditions for the regularity and the singularity for 0<α≦2, using known results on the invariant subspaces. We also get Cramér-Wold decomposition for the case 0<α≦2.
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Supported by CPBP01. 02.
Supported by ONR N00014-85-K-0150
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Makagon, A., Mandrekar, V. The spectral representation of stable processes: Harmonizability and regularity. Probab. Th. Rel. Fields 85, 1–11 (1990). https://doi.org/10.1007/BF01377623
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DOI: https://doi.org/10.1007/BF01377623
Keywords
- Stochastic Process
- Probability Theory
- Classical Representation
- Mathematical Biology
- Average Process