Strong convergence of infinite color balanced urns under uniform ergodicity
Journal of Applied Probability
We consider the generalization of the Pólya urn scheme with possibly infinitely many colors, as introduced in , , , and . For countably many colors, we prove almost sure convergence of the urn configuration under the uniform ergodicity assumption on the associated Markov chain. The proof uses a stochastic coupling of the sequence of chosen colors with a branching Markov chain on a weighted random recursive tree as described in , , and . Using this coupling we estimate the covariance between any two selected colors. In particular, we re-prove the limit theorem for the classical urn models with finitely many colors.
Bandyopadhyay, Antar; Janson, Svante; and Thacker, Debleena, "Strong convergence of infinite color balanced urns under uniform ergodicity" (2020). Journal Articles. 142.