Central limit theorems for a hypergeometric randomly reinforced urn
TLDR
Some central limit theorems in the sense of stable convergence and of almost sure conditional convergence are proved, which are stronger than convergence in distribution.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.read more
Citations
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Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria
Ido Erev,Alvin E. Roth +1 more
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A survey of random processes with reinforcement
TL;DR: The models surveyed in this paper include generalized Polya urns, reinforced random walks, interacting urn models, and continuous reinforced processes, with a focus on methods and results, with sketches provided of some proofs.