Spreading and Predictable Sampling for Exchangeable Sequences and Processes

摘要

Rydll-Nardzewski (1957) proved that an infinite sequence of random variables is exchangeable, if every subsequence has the same distribution. This document discusses some restatements and extensions of this result in terms of martingales and stopping times. In the other direction, it is shown 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. (Author)