Journal of Applied Probability: Volume 45 - Issue 4

Chaoticity for Multiclass Systems and Exchangeability Within Classes
Part of:
Carl Graham
Published online by Cambridge University Press:

14 July 2016, pp. 1196-1203
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Classical results for exchangeable systems of random variables are extended to multiclass systems satisfying a natural partial exchangeability assumption. It is proved that the conditional law of a finite multiclass 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 independent and identically distributed system implies asymptotic independence between {different} classes. A result implying the Hewitt-Savage 0-1 law is also extended.

Journal of Applied Probability