Large deviations for a triangular array of exchangeable random variables

ABSTRACT. – In this paper we consider a triangular array whose rows are composed of finite exchangeable random variables. We prove that, under suitable conditions, the sequence defined by the empirical measure process of each row satisfies a large deviation principle. We first study the particular case where the rows are given by sampling without replacement from fixed urns. Then we prove a large deviation principle in the general setting, by identifying finite exchangeable random variables and sampling without replacement from urns with random composition. 2002 Éditions scientifiques et médicales Elsevier SAS AMS classification: Primary 60F10; secondary 60G09 and 62G0