The Annals of Probability

Spreading and Predictable Sampling in Exchangeable Sequences and Processes

Olav Kallenberg

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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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Ann. Probab., Volume 16, Number 2 (1988), 508-534.

First available in Project Euclid: 19 April 2007

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Zentralblatt MATH identifier


Primary: 60G99: None of the above, but in this section
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60G44: Martingales with continuous parameter

Invariance in distribution subsequences thinning stationarity predictable stopping times allocation sequences and processes semimartingales local characteristics stochastic integrals


Kallenberg, Olav. Spreading and Predictable Sampling in Exchangeable Sequences and Processes. Ann. Probab. 16 (1988), no. 2, 508--534. doi:10.1214/aop/1176991771.

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