An algebraic approach to Polya processes

Nicolas Pouyanne (1)

1 LMV - Laboratoire de Mathématiques de Versailles

Pólya processes are natural generalization of Pólya-Eggenberger urn models. This article presents a new approach of their asymptotic behaviour {\it via} moments, based on the spectral decomposition of a suitable finite difference operator on polynomial functions. Especially, it provides new results for {\it large} processes (a Pólya process is called {\it small} when $1$ is simple eigenvalue of its replacement matrix and when any other eigenvalue has a real part $\leq 1/2$; otherwise, it is called large).

Mots clés: Polya urns; Polya process; martingale; moments

Domaines: Combinatoire [math.CO]; Probabilités [math.PR]; Mathématique discrète [cs.DM]; Algorithme et structure de données [cs.DS]

Nicolas Pouyanne. An algebraic approach to Polya processes. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2008, pp.Vol. 44, No. 2, 293-323. ⟨hal-00004597v3⟩