A martingale approach for Pólya urn processes

2020/03/10 by Lucile Laulin, Laulin, Lucile
Mathematics · Physics and Astronomy · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2003.04592

openalex publication_date 2020/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to a direct martingale approach for Pólya urn models asymptotic behaviour. A Pólya process is said to be small when the ratio of its remplacement matrix eigenvalues is less than or equal to 1/2, otherwise it is called large. We find again some well-known results on the asymptotic behaviour for small and large urns processes. We also provide new almost sure properties for small urns processes.

Citations

• Analytic urns

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