?url_ver=Z39.88-2004&rft_id=arXiv%3A1705.02126&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Feprints.imtlucca.it%2F3701%2F&rft.title=Networks+of+reinforced+stochastic+processes%3A+Asymptotics+for+the+empirical+means&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=This+work+deals+with+systems+of+interacting+reinforced+stochastic+processes%2C+where+each+process+X%5Ej+%3D+(X_%7Bn%2Cj%7D)_n+is+located+at+a+vertex+j+of+a+finite+weighted+direct+graph%2C+and+it+can+be+interpreted+as+the+sequence+of+%E2%80%9Cactions%E2%80%9D+adopted+by+an+agent+j+of+the+network.+The+interaction%0D%0Aamong+the+evolving+dynamics+of+these+processes+depends+on+the+weighted+adjacency+matrix+W+associated+to+the+underlying+graph%3A+indeed%2C+the+probability+that+an+agent+j+chooses+a+certain+action+depends+on+its+personal+%E2%80%9Cinclination%E2%80%9D+Z_%7Bn%2Cj%7D++and+on+the+inclinations+Z_%7Bn%2Ch%7D+%2C+with+h+not+equal+to+j%2C+of+the+other+agents+according+to+the+elements+of+W.%0D%0AAsymptotic+results+for+the+stochastic+processes+of+the+personal+inclinations+Z%5Ej+%3D+(Z_%7Bn%2Cj%7D)_n+have%0D%0Abeen+subject+of+studies+in+recent+papers+(e.g.+%5B2%2C+21%5D)%3B+while+the+asymptotic+behavior+of+the+stochastic%0D%0Aprocesses+of+the+actions+(X_%7Bn%2Cj%7D)_n+has+never+been+studied+yet.+In+this+paper%2C+we+fill+this+gap+by+characterizing+the+asymptotic+behavior+of+the+empirical+means+N_%7Bn%2Cj%7D+%3D+%5Csum_%7Bk%3D1%7D%5En+X_%7Bk%2Cj%7D+%2Fn%2C+proving+their+almost+sure+synchronization+and+some+central+limit+theorems+in+the+sense+of+stable+convergence.+Moreover%2C+we+discuss+some+statistical+applications+of+these+convergence+results+concerning+confidence+intervals+for+the+random+limit+toward+which+all+the+processes+of+the+system+converge+and+tools+to%0D%0Amake+inference+on+the+matrix+W.&rft.date=2017&rft.type=Working+Paper&rft.type=NonPeerReviewed&rft.identifier=++Aletti%2C+Giacomo+and+Crimaldi%2C+Irene+and+Ghiglietti%2C+Andrea++Networks+of+reinforced+stochastic+processes%3A+Asymptotics+for+the+empirical+means.++Technical+Report+++++++(Submitted)+++&rft.relation=https%3A%2F%2Farxiv.org%2Fabs%2F1705.02126&rft.relation=arXiv%3A1705.02126