We consider systems of interacting Generalized Friedman’s Urns (GFUs) having irreducible mean replacement matrices. The interaction is modeled through the probability to sample the colors from each urn, that is defined as convex combination of the urn proportions in the system. From the weights of these combinations we individuate subsystems of urns evolving with different behaviors. We provide a complete description of the asymptotic properties of urn proportions in each subsystem by establishing limiting proportions, convergence rates and Central Limit Theorems. The main proofs are based on a detailed eigenanalysis and stochastic approximation techniques.

Interacting generalized Friedman’s urn systems / G. Aletti, A. Ghiglietti. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - 127:8(2017 Aug), pp. 2650-2678. [10.1016/j.spa.2016.12.003]

Interacting generalized Friedman’s urn systems

G. Aletti
Primo
;
A. Ghiglietti
2017

Abstract

We consider systems of interacting Generalized Friedman’s Urns (GFUs) having irreducible mean replacement matrices. The interaction is modeled through the probability to sample the colors from each urn, that is defined as convex combination of the urn proportions in the system. From the weights of these combinations we individuate subsystems of urns evolving with different behaviors. We provide a complete description of the asymptotic properties of urn proportions in each subsystem by establishing limiting proportions, convergence rates and Central Limit Theorems. The main proofs are based on a detailed eigenanalysis and stochastic approximation techniques.
Interacting systems; Urn models; Strong consistency; Central Limit Theorems; Stochastic approximation
Settore MAT/06 - Probabilita' e Statistica Matematica
Settore SECS-S/01 - Statistica
ago-2017
Centro di Ricerca Interdisciplinare su Modellistica Matematica, Analisi Statistica e Simulazione Computazionale per la Innovazione Scientifica e Tecnologica ADAMSS
http://hdl.handle.net/2434/353772
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/464155
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