Stable mixed moving averages
type: Item
instance of: scholarly article
title: Stable mixed moving averages
zbMATH Open document ID: 0794.60026
DOI: 10.1007/BF01192963
author: Donatas Surgailis
author: Stamatis Cambanis
author: Jan Rosiński
author: V. S. Mandrekar
publication date: 1994-08-15T00:00:00Z
review text: The class of (non-Gaussian) stable moving average processes is extended by introducing an appropriate joint randomization of the filter function and of the stable noise, leading to stable mixed moving averages. Their distribution determines a certain combination of the filter function and the mixing measure, leading to a generalization of a theorem of \textit{M. Kanter} [Trans. Am. Math. Soc. 179, 35-47 (1973; Zbl 0271.43007)] for usual moving averages. Stable mixed moving averages contain sums of independent stable moving averages, are ergodic and are not harmonizable. Also a class of stable mixed moving averages is constructed with the reflection positivity property.
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60B05
zbMATH DE Number: 569002
zbMATH Keywords: spectral representation
zbMATH Keywords: stable moving average processes
zbMATH Keywords: mixing measure
zbMATH Keywords: mixed moving averages
zbMATH Keywords: reflection positivity property
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569002