A martingale approach for P\'olya urn processes

Lucile Laulin

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arXiv · 2003.04592

A martingale approach for P\'olya urn processes

Lucile Laulin

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Abstract

This paper is devoted to a direct martingale approach for P{\'o}lya urn models asymptotic behaviour. A P{\'o}lya process is said to be small when the ratio of its remplacement matrix eigenvalues is less than or equal to 1/2, otherwise it is called large. We find again some well-known results on the asymptotic behaviour for small and large urns processes. We also provide new almost sure properties for small urns processes.

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Lucile Laulin. 2020-03-10. A martingale approach for P\'olya urn processes. https://arxiv.org/abs/2003.04592

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