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On the distribution of the limit proportion for a two-color, randomly reinforced urn with equal reinforcement distributions

Part of: Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  01 July 2016

Giacomo Aletti ,
Caterina May  and
Piercesare Secchi
Giacomo Aletti*
Affiliation:
Università degli Studi di Milano
Caterina May*
Affiliation:
Università degli Studi di Milano
Piercesare Secchi*
Affiliation:
Politecnico di Milano
*
∗ Postal address: Dipartimento di Matematica ‘F. Enriques’, Università degli Studi di Milano, Via C. Saldini, 50, I-20133 Milano, Italy.
∗ Postal address: Dipartimento di Matematica ‘F. Enriques’, Università degli Studi di Milano, Via C. Saldini, 50, I-20133 Milano, Italy.
∗∗ Postal address: MOX - Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy. Email address: piercesare.secchi@polimi.it
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Abstract

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We consider a two-color, randomly reinforced urn with equal reinforcement distributions and we characterize the distribution of the urn's limit proportion as the unique continuous solution of a functional equation involving unknown probability distributions on [0, 1].

Keywords

Generalized Polya's urn sequencefunctional equation in unknown distribution functionsreinforced urn processrandomized response adaptive design of experiments

MSC classification

Primary: 60B10: Convergence of probability measures
Secondary: 39B52: Equations for functions with more general domains and/or ranges
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 39 , Issue 3 , September 2007 , pp. 690 - 707
Copyright
Copyright © Applied Probability Trust 2007 

References

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