Cécile Mailler

Measure-valued Pólya processes

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 $\{1, \ldots, d\}$. 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 $1\leq i\leq d$. 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.