A.s. convergence for infinite colour P\'olya urns associated with random walks

Svante Janson

A.s. convergence for infinite colour P\'olya urns associated with random walks

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arxiv 1803.04207 v1 pith:GOKRDYOW submitted 2018-03-12 math.PR

Svante Janson This is my paper · ORCID

classification math.PR

keywords convergencedistributionassumingcolourolyarandomurnsassociated

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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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