Exactly Solvable Balanced Tenable Urns with Random Entries via the Analytic Methodology

Basile Morcrette; Hosam M. Mahmoud

hal-00719639, version 1

Exactly Solvable Balanced Tenable Urns with Random Entries via the Analytic Methodology

Basile Morcrette (, ) ^1, 2, Hosam M. Mahmoud ³

AofA'12 - 23rd International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms AQ (2012) pp. 219--232

Résumé : This paper develops an analytic theory for the study of some Polya urns with random rules. The idea is to extend the isomorphism theorem in Flajolet et al. (2006), which connects deterministic balanced urns to a differential system for the generating function. The methodology is based upon adaptation of operators and use of a weighted probability generating function. Systems of differential equations are developed, and when they can be solved, they lead to characterization of the exact distributions underlying the urn evolution. We give a few illustrative examples.

1 : Laboratoire d'Informatique de Paris 6 (LIP6)
CNRS : UMR7606 – Université Pierre et Marie Curie [UPMC] - Paris VI
2 : ALGORITHMS (INRIA Rocquencourt)
INRIA
3 : Department of Statistics [Washington] (Columbian College of Arts and Sciences)
George Washington University

hal-00719639, version 1
http://hal.archives-ouvertes.fr/hal-00719639
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Contributeur : Basile Morcrette <>
Soumis le : Vendredi 20 Juillet 2012, 13:41:32
Dernière modification le : Vendredi 24 Août 2012, 14:51:10

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