Rate of Convergence and Large Deviation for the Infinite Color Pólya Urn Schemes

2013/10/21 by Antar Bandyopadhyay, Bandyopadhyay, Antar, Debleena Thacker +1
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR

paper · pdf · doi:10.48550/arxiv.1310.5751

13 pages

arxiv created 2013/10/21 · arxiv updated 2013/10/23

Abstract

In this work we consider the infinite color urn model associated with a bounded increment random walk on \Zbold^d. This model was first introduced by Bandyopadhyay and Thacker (2013). We prove that the rate of convergence of the expected configuration of the urn at time n with appropriate centering and scaling is of the order \mathcal O((1)/(√(log n))). Moreover we derive bounds similar to the classical Berry-Essen bound. Further we show that for the expected configuration a large deviation principle (LDP) holds with a good rate function and speed log n.

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