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Measure-valued P\'olya urn processes (with Jean-François Marckert)

Banff International Research Station for Mathematical Innovation and Discovery

A P\'olya 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.

Mathematics; Combinatorics; Probability theory and stochastic processes; Control/optimization/operation research

video/mp4

Author affiliation: University of Bath

2017-04-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61399

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/