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A New Approach to Pólya Urn Schemes and Its Infinite Color Generalization

2016/06/16 by Antar Bandyopadhyay, Bandyopadhyay, Antar, Debleena Thacker +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1606.05317

openalex publication_date 2016/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we generalize Polya urn schemes with possibly infinitely many colors and extend the earlier models described in [4, 5, 7]. We provide a novel and unique approach of representing the observed sequence of colors in terms a branching Markov chain on random recursion tree. This enables us to derive fairly general asymptotic for our urn schemes. We then illustrate through several examples that our method can easily derive the classical results for finite urns, as well as, many new results for infinite color urns.

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