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Interacting reinforced-urn systems

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Anna Maria Paganoni  and
Piercesare Secchi
Anna Maria Paganoni*
Affiliation:
Politecnico di Milano
Piercesare Secchi*
Affiliation:
Politecnico di Milano
*
∗ Postal address: Dipartimento di Matematica ‘F. Brioschi', Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20123 Milano, Italy.
∗ Postal address: Dipartimento di Matematica ‘F. Brioschi', Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20123 Milano, Italy.
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Abstract

We introduce a class of discrete-time stochastic processes generated by interacting systems of reinforced urns. We show that such processes are asymptotically partially exchangeable and we prove a strong law of large numbers. Examples and the analysis of particular cases show that interacting reinforced-urn systems are very flexible representations for modelling countable collections of dependent and asymptotically exchangeable sequences of random variables.

Keywords

Urn modelreinforcementPólya urn

MSC classification

Primary: 60F15: Strong theorems
Secondary: 60G09: Exchangeability
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 3 , September 2004 , pp. 791 - 804
Copyright
Copyright © Applied Probability Trust 2004 

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