Decomposition of discrete time periodically correlated and multivariate stationary symmetric stable processes

The spectral structure of discrete time periodically correlated (as well as multivariate stationary) symmetric α -stable processes is identified by decomposing such a process uniquely in distribution into one sum of three mutually independent periodically correlated (multivariate stationary) stable...

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Bibliographic Details
Published in:Stochastic processes and their applications 2005-11, Vol.115 (11), p.1838-1859
Main Authors: Soltani, A.R., Parvardeh, A.
Format: Article
Language:English
Subjects:
Cocycle
Exact sciences and technology
Flow
Hopf decomposition
Mathematics
Mixed moving average
Multivariate stationary stable processes
Periodically correlated harmonizable processes
Periodically correlated stable processes
Periodically correlated stable processes Multivariate stationary stable processes Spectral representation Mixed moving average Periodically correlated harmonizable processes Flow Cocycle Hopf decomposition
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Spectral representation
Stochastic processes
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Summary:The spectral structure of discrete time periodically correlated (as well as multivariate stationary) symmetric α -stable processes is identified by decomposing such a process uniquely in distribution into one sum of three mutually independent periodically correlated (multivariate stationary) stable processes that are classified as mixed moving average, harmonizable and of a third kind. The techniques are based on presenting the flow and its cocycle that govern the spectral representation of the process, using the Hopf decomposition and specifying the harmonizable component.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2005.06.005