Journal of Applied Probability

Central limit theorems for a hypergeometric randomly reinforced urn

Irene Crimaldi

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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.

Article information

Source
J. Appl. Probab., Volume 53, Number 3 (2016), 899-913.

Dates
First available in Project Euclid: 13 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1476370784

Mathematical Reviews number (MathSciNet)
MR3570102

Zentralblatt MATH identifier
1351.60024

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G57: Random measures 60B10: Convergence of probability measures 60G42: Martingales with discrete parameter

Keywords
Central limit theorem Pòlya urn preferential attachment random process with reinforcement randomly reinforced urn stable convergence

Citation

Crimaldi, Irene. Central limit theorems for a hypergeometric randomly reinforced urn. J. Appl. Probab. 53 (2016), no. 3, 899--913. https://projecteuclid.org/euclid.jap/1476370784


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