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Probability Seminars

Limits of Polya urns with innovations

With Jean Bertoin (Zurich)

Limits of Polya urns with innovations

We consider a version of the classical P’olya urn scheme which incorporates innovations. The space $S$ of colors is an arbitrary measurable set.
After each sampling of a ball in the urn, one returns $C$ balls of the same color and additional balls of different colors given by some finite point process $xi$ on $S$.
When the number of steps goes to infinity, the empirical distribution of the colors in the urn converges to the normalized intensity measure of $xi$, and we analyze the fluctuations.
The ratio $rho= E©/E®$ of the average number of copies to the average total number of balls returned plays a key role.

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