Measure-valued Pólya processes

Cécile Mailler (University of Bath)

Friday 24th November, 2017 15:00-16:00 Seminar room 110

Abstract

A Pólya urn is a stochastic process that describes the composition of an urn that contains balls of different colours.  The set of colours is usually a finite set {1, ..., d}. At each discrete-time step, one draws a ball uniformly at random in the urn (let c be its colour),  and replace it in the urn together with R_{c,i} balls of colour i, for all 1 ≤ i ≤ d.

In this talk, I will present a generalisation of this model to an infinite, and potentially uncountable set of colours. In this new framework, the composition of the urn is a measure (possibly non-atomic) on a Polish space.

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