Theoretical Statistics and Mathematics Unit, ISI Delhi

Rate of Convergence and Large Deviation for the Infinite Color P\'olya Urn Schemes

by Antar Bandyopadhyay and Debleena Thacker

In this work we consider the \emph{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 ${\mathcal O}\left(\frac{1}{\sqrt{\log n}}\right)$. Moreover we derive bounds similar to the classical Berry-Essen bound. Further we show that for the expected configuration a \emph{large deviation principle (LDP)} holds with a good rate function and speed $\log n$.

isid/ms/2013/13 [fulltext]

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