We consider a system of interacting Generalized P\'olya Urns (GPUs) 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.
|Titolo:||Interacting Generalized Pólya Urn Systems|
ALETTI, GIACOMO (Primo)
|Parole Chiave:||Interacting systems; Generalized Polya urn models; Central Limit Theorems; Strong Consistency; Stochastic approximation|
|Settore Scientifico Disciplinare:||Settore MAT/06 - Probabilita' e Statistica Matematica|
|Data di pubblicazione:||2016-01-07|
|Appare nelle tipologie:||24 - Pre-print|