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An algebraic approach to Polya processes

Nicolas Pouyanne
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Abstract

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).

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Nicolas Pouyanne. 2009-07-11. An algebraic approach to Polya processes. https://doi.org/10.1214/07-aihp130

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