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arXiv 2003.045922020-03-10math.PR

A martingale approach for Pólya urn processes

Lucile Laulin

英文摘要：

This paper is devoted to a direct martingale approach for P{ó}lya urn models asymptotic behaviour. A P{ó}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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