Chaoticity for multi-class systems and exchangeability within classes

Details Chaoticity for multi-class systems and exchangeability within classes Chaoticity for multi-class systems and exchangeability within classes

2007-09-12

arxiv.org/abs/0709.1918v4

Mathematics

Probability

Third revision, v4. The paper is similar to the second revision v3, with several improvements

Scientific paper

Classical results for exchangeable systems of random variables are extended to multi-class systems satisfying a natural partial exchangeability assumption. It is proved that the conditional law of a finite multi-class system, given the value of the vector of the empirical measures of its classes, corresponds to independent uniform orderings of the samples within each class, and that a family of such systems converges in law if and only if the corresponding empirical measure vectors converge in law. As a corollary, convergence within each class to an infinite i.i.d. system implies asymptotic independence between different classes. A result implying the Hewitt-Savage 0-1 Law is also extended.

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