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September 2016 Central limit theorems for a hypergeometric randomly reinforced urn
Irene Crimaldi
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J. Appl. Probab. 53(3): 899-913 (September 2016).

Abstract

We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number of extracted balls of a certain color, given the past, is assumed to be hypergeometric. We prove some central limit theorems in the sense of stable convergence and of almost sure conditional convergence, which are stronger than convergence in distribution. The proven results provide asymptotic confidence intervals for the limit proportion, whose distribution is generally unknown. Moreover, we also consider the case of more urns subjected to some random common factors.

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Irene Crimaldi. "Central limit theorems for a hypergeometric randomly reinforced urn." J. Appl. Probab. 53 (3) 899 - 913, September 2016.

Information

Published: September 2016
First available in Project Euclid: 13 October 2016

zbMATH: 1351.60024
MathSciNet: MR3570102

Subjects:
Primary: 60F05
Secondary: 60B10, 60G42, 60G57

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 3 • September 2016
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