Random replacements in pólya urns with infinitely many colours

Abstract

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  S×[0,1] .