The Annals of Probability

Spreading and Predictable Sampling in Exchangeable Sequences and Processes

Olav Kallenberg

Full-text: Open access

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991771

Digital Object Identifier
doi:10.1214/aop/1176991771

Mathematical Reviews number (MathSciNet)
MR929061

Zentralblatt MATH identifier
0649.60043

JSTOR
links.jstor.org

Subjects
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

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

Citation

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


Export citation