?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F3521%2F&rft.title=Synchronization+of+Reinforced+Stochastic+Processes+with+a+Network-based+Interaction&rft.creator=Aletti%2C+Giacomo&rft.creator=Crimaldi%2C+Irene&rft.creator=Ghiglietti%2C+Andrea&rft.subject=HA+Statistics&rft.subject=QA+Mathematics&rft.description=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%2C+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%2C+that+recently+has+been+introduced+in+Crimaldi+et+al.+(2016%2C+arXiv%3A1602.06217).+Generally+speaking%2C+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%2C+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.&rft.publisher=arXiv&rft.date=2016&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.identifier=++Aletti%2C+Giacomo+and+Crimaldi%2C+Irene+and+Ghiglietti%2C+Andrea++Synchronization+of+Reinforced+Stochastic+Processes+with+a+Network-based+Interaction.++Technical+Report+++arXiv+++++++(Submitted)+++&rft.relation=http%3A%2F%2Farxiv.org%2Fabs%2F1607.08514