## The Annals of Probability

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

### Spreading and Predictable Sampling in Exchangeable Sequences and Processes

#### 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