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April, 1988 Spreading and Predictable Sampling in Exchangeable Sequences and Processes
Olav Kallenberg
Ann. Probab. 16(2): 508-534 (April, 1988). DOI: 10.1214/aop/1176991771


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.


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Olav Kallenberg. "Spreading and Predictable Sampling in Exchangeable Sequences and Processes." Ann. Probab. 16 (2) 508 - 534, April, 1988.


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

zbMATH: 0649.60043
MathSciNet: MR929061
Digital Object Identifier: 10.1214/aop/1176991771

Primary: 60G99
Secondary: 60G40 , 60G44

Keywords: allocation sequences and processes , Invariance in distribution , local characteristics , predictable stopping times , Semimartingales , stationarity , stochastic integrals , subsequences , thinning

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 2 • April, 1988
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