Strong Convergence of Infinite Color Balanced Urns Under Uniform Ergodicity
| Autor: | Bandyopadhyay, Antar, Janson, Svante, Thacker, Debleena |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Journal of Applied Probability, 57(3): 853 - 865 2020 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/jpr.2020.37 |
| Popis: | We consider the generalization of the P\'olya urn scheme with possibly infinite many colors as introduced in \cite{Th-Thesis, BaTH2014, BaTh2016, BaTh2017}. For countable many colors, we prove almost sure convergence of the urn configuration under \emph{uniform ergodicity} assumption on the associated Markov chain. The proof uses a stochastic coupling of the sequence of chosen colors with a \emph{branching Markov chain} on a weighted \emph{random recursive tree} as described in \cite{BaTh2017, Sv_2018}. Using this coupling we estimate the covariance between any two selected colors. In particular, we reprove the limit theorem for the classical urn models with finitely many colors. Comment: 13 pages |
| Databáze: | arXiv |
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