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Random replacements in Pólya urns with infinitely many colours. (English) Zbl 1412.60021
Summary: We consider the general version of Pólya urns recently studied by A. Bandyopadhyay and D. Thacker [“A new approach to Pólya urn schemes and its infinite color generalization”, Preprint, arXiv:1606.05317; Bernoulli 23, No. 4B, 3243–3267 (2017; Zbl 1407.60099)] and C. Mailler and J.-F. Marckert [Electron. J. Probab. 22, Paper No. 26, 33 p. (2017; Zbl 1358.60091)], with the space of colours being any Borel space $$S$$ and the state of the urn being a finite measure on $$S$$. We consider urns with random replacements, and show that these can be regarded as urns with deterministic replacements using the colour space $$S\times [0,1]$$.

##### MSC:
 60C05 Combinatorial probability
##### Keywords:
Pólya urn; infinite Pólya urn; random replacements
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##### References:
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