TY  - RPRT
M1  - technical_report
N2  - Randomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon, that could be roughly defined as the tendency of different components to adopt a common behavior. We continue the study of a model of interacting stochastic processes with reinforcement, that recently has been introduced in Crimaldi et al. (2016, arXiv:1602.06217). Generally speaking, by reinforcement we mean any mechanism for which the probability that a given event occurs has an increasing dependence on the number of times that events of the same type occurred in the past. The particularity of systems of such stochastic processes is that synchronization is induced along time by the reinforcement mechanism itself and does not require a large-scale limit. We focus on the relationship between the topology of the network of the interactions and the long-time synchronization phenomenon. After proving the almost sure synchronization, we provide some CLTs in the sense of stable convergence that establish the convergence rates and the asymptotic distributions for both convergence to the common limit and synchronization. The obtained results lead to the construction of asymptotic confidence intervals for the limit random variable and of statistical tests to make inference on the topology of the network given the observation of the reinforced stochastic processes positioned at the vertices.
ID  - eprints3521
KW  - Keywords: Interacting Systems; Reinforced Stochastic Processes; Urn Models; Complex Networks; Synchronization; Asymptotic Normality. - 
2010 AMS classification: 60F05
KW  -  60F15
KW  -  60K35
KW  -  62P35
KW  -  91D30
AV  - none
EP  - 40
UR  - http://arxiv.org/abs/1607.08514
PB  - arXiv
A1  - Aletti, Giacomo
A1  - Crimaldi, Irene
A1  - Ghiglietti, Andrea
TI  - Synchronization of Reinforced Stochastic Processes with a Network-based Interaction
Y1  - 2016///
ER  -