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January, 1988 A De Finetti Theorem for a Class of Pairwise Independent Stationary Processes
James B. Robertson, Stephen Simons
Ann. Probab. 16(1): 344-354 (January, 1988). DOI: 10.1214/aop/1176991906


Consider a $\{0, 1\}$-valued strictly stationary stochastic process $\{X_1,X_2,\ldots\}$. Let $k$ and $l$ be natural numbers and define $y_i = 0$ or 1 according as $x_1 + \cdots + x_{i+k-1}$ is even or odd. Then, for $1 \leq j \leq l$ set $S_j(x_1 \cdots x_n) = \sum_{0\leq i \leq m - 1}y_{j+il}$. We consider all processes that have $(S_1,\ldots,S_l)$ as sufficient statistics. We obtain explicit formulas for the distributions of the processes that are extreme points. We also represent these processes as finitary processes and use this representation to investigate their pairwise independence, ergodicity and mixing properties.


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James B. Robertson. Stephen Simons. "A De Finetti Theorem for a Class of Pairwise Independent Stationary Processes." Ann. Probab. 16 (1) 344 - 354, January, 1988.


Published: January, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0636.60033
MathSciNet: MR920276
Digital Object Identifier: 10.1214/aop/1176991906

Primary: 60G10
Secondary: 28D05

Keywords: de Finetti theorem , Ergodic , extreme point of compact convex set , finitary process , pairwise independence , stationary stochastic process , weakly mixing

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 1 • January, 1988
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