A de Finetti theorem for a class of pairwise independent stationary processes
type: Item
instance of: scholarly article
title: A de Finetti theorem for a class of pairwise independent stationary processes
zbMATH Open document ID: 0636.60033
author: James B. Robertson
author: Stephen Simons
published in: The Annals of Probability
publication date: 1988-01-01T00:00:00Z
review text: Let \(X_ n\), \(n=1,2,...\), be a stochastic process such that \(P\{X_ n=0\}=P\{X_ n=1\}=1/2\). A one-parameter family of distributions for pairwise independent, ergodic stationary stochastic processes of this kind was constructed as well as sufficient statistics for this parameter were calculated by the first author [Math. Sci. 10, 109-117 (1985; Zbl 0583.60031)]. The authors consider generalizations of these sufficient statistics and, among other results, describe all the processes with these sufficient statistics. Pairwise independent and ergodic processes are identified. Extreme point methods for convex sets are applied, especially the authors make use of a representation theorem by \textit{P. Ressel} [Ann. Probab. 13, 898-922 (1985; Zbl 0579.60012)].
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 4036815
zbMATH Keywords: de Finetti theorem
zbMATH Keywords: ergodic stationary stochastic processes
zbMATH Keywords: Extreme point methods for convex sets
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991906
OpenAlex ID: W2070398936
DOI: 10.1214/AOP/1176991906
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description: scientific article; zbMATH DE number 4036815