Random replacements in Pólya urns with infinitely many colours

[摘要] We consider the general version of Pólya urns recently studied by Bandyopadhyay and Thacker (2016+) and Mailler and Marckert (2017), 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 $Simes [0,1]$.

[学科分类] 统计和概率

[关键词] Pólya urn;infinite Pólya urn;random replacements