A.s. convergence for infinite colour P\'olya urns associated with random walks
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Publication:6298926
DOI10.4310/ARKIV.2021.V59.N1.A4arXiv1803.04207MaRDI QIDQ6298926
Publication date: 12 March 2018
Abstract: We consider P'olya urns with infinitely many colours that are of a random walk type, in two related version. We show that the colour distribution a.s., after rescaling, converges to a normal distribution, assuming only second moments on the offset distribution. This improves results by Bandyopadhyay and Thacker (2014--2017; convergence in probability), and Mailler and Marckert (2017; a.s. convergence assuming exponential moment).
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