Ryll-Nardzewski has proved that an infinite sequence of random variables is exchangeable if every subsequence has the same distribution. We discuss some restatements and extensions of this result in terms of martingales and stopping times. In the other direction, we show that the distribution of a finite or infinite exchangeable sequence is invariant under sampling by means of a.s. distinct (but not necessarily ordered) predictable stopping times. Both types of result generalize to exchangeable processes in continuous time.
Publié le : 1988-04-14
Classification:
Invariance in distribution,
subsequences,
thinning,
stationarity,
predictable stopping times,
allocation sequences and processes,
semimartingales,
local characteristics,
stochastic integrals,
60G99,
60G40,
60G44
@article{1176991771,
author = {Kallenberg, Olav},
title = {Spreading and Predictable Sampling in Exchangeable Sequences and Processes},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 508-534},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991771}
}
Kallenberg, Olav. Spreading and Predictable Sampling in Exchangeable Sequences and Processes. Ann. Probab., Tome 16 (1988) no. 4, pp. 508-534. http://gdmltest.u-ga.fr/item/1176991771/