Convergence of multi-class systems of fixed possibly infinite sizes

Details Convergence of multi-class systems of fixed possibly infinite sizes Convergence of multi-class systems of fixed possibly infinite sizes

2009-02-03

arxiv.org/abs/0902.0539v1

Mathematics

Probability

Scientific paper

Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of its finite classes and directing measures of its infinite ones (given by the de Finetti Theorem), corresponds to sampling independently from each class, without replacement from the finite classes and i.i.d. from the directing measure for the infinite ones. The equivalence between the convergence of multi-exchangeable systems with fixed class sizes and the convergence of the corresponding vectors of measures is then established.

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