Periodicity and absolute regularity
type: Item
instance of: scholarly article
title: Periodicity and absolute regularity
zbMATH Open document ID: 0613.60033
DOI: 10.1007/BF02765027
author: Henry Berbee
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: [A previous version of the paper has been reviewed in Zbl 0533.60038.] The ''total variation'' properties similar to 0-2 theorem for Markov chains are proved for a general ergodic stationary sequence \(\xi\). The conditions for the periodicity are given. It shows that when the period p is finite, the double tail \(\sigma\)-field of \(\xi\) is partitioned into atoms which are \(T^ p\)-invariant, and when \(p=1\), \(\xi\) is absolutely regular.
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 3992542
zbMATH Keywords: absolute regularity
zbMATH Keywords: variation of a signed measure
zbMATH Keywords: ergodic stationary sequence
zbMATH Keywords: periodicity
reviewed by: Minping Qian
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3992542