A.s. convergence for infinite colour Pólya urns associated with random walks

2018/03/12 by Janson, Svante
#60C05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1803.04207

Abstract

We consider Pólya 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).

Cited by

• Some developments of exchangeable measure-valued Pólya sequences

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