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.
Publié le : 1988-01-14
Classification:
de Finetti theorem,
stationary stochastic process,
finitary process,
pairwise independence,
ergodic,
weakly mixing,
extreme point of compact convex set,
60G10,
28D05
@article{1176991906,
author = {Robertson, James B. and Simons, Stephen},
title = {A De Finetti Theorem for a Class of Pairwise Independent Stationary Processes},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 344-354},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991906}
}
Robertson, James B.; Simons, Stephen. A De Finetti Theorem for a Class of Pairwise Independent Stationary Processes. Ann. Probab., Tome 16 (1988) no. 4, pp. 344-354. http://gdmltest.u-ga.fr/item/1176991906/