Chaoticity for multi-class systems and exchangeability within classes

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

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Probability, 60K35 (Primary), 60B10, 60G09, 62B05 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/171521

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0709.1918
 http://arxiv.org/abs/0709.1918

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arXiv