A New Randomized Pólya Urn Model


In this paper, we propose a new class of discrete time stochastic processes generated by a two-color generalized Pólya urn, that is reinforced every time. A single urn contains a white balls, b black balls and evolves as follows: at discrete times n=1,2,…, we sample Mn balls and note their colors, say Rn are white and Mn- Rn are black. We return the drawn balls in the urn. Moreover, NnRn new white balls and Nn (Mn- Rn) new black balls are added in the urn. The numbers Mn and Nn are random variables. We show that the proportions of white balls forms a bounded martingale sequence which converges almost surely. Necessary and sufficient conditions for the limit to concentrate on the set {0,1} are given.

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D. Aoudia and F. Perron, "A New Randomized Pólya Urn Model," Applied Mathematics, Vol. 3 No. 12A, 2012, pp. 2118-2122. doi: 10.4236/am.2012.312A292.

Conflicts of Interest

The authors declare no conflicts of interest.


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