Abstract
We consider Pólya urns with infinitely many colours that are of a random walk type, in two related versions. 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).
Funding Statement
Partly supported by the Knut and Alice Wallenberg Foundation.
Citation
Svante Janson. "A.s. convergence for infinite colour Pólya urns associated with random walks." Ark. Mat. 59 (1) 87 - 123, April 2021. https://doi.org/10.4310/ARKIV.2021.v59.n1.a4
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