?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4980%2F&rft.title=The+Rise+of+Complex+Beliefs+Dynamics&rft.creator=Barucci%2C+E.&rft.creator=Posch%2C+M.&rft.description=We+prove+that+complex+beliefs+dynamics+may+emerge+in+linear+stochastic+models+as+the+outcome+of+bounded+rationality+learning.+If+agents+believe+in+a+misspecified+law+of+motion+(which+is+correctly+specified+at+the+Rational+Expectations+Equilibria+of+the+model)+and+update+their+beliefs+observing+the+evolving+economy%2C+their+beliefs+can+follow+in+the+limit+a+beliefs+cycle+which+is+not+a+self-fulfilling+solution+of+the+model.+The+stochastic+process+induced+by+the+learning+rule+is+analyzed+by+means+of+an+associated+ordinary+differential+equation+(ODE).+The+existence+of+a+uniformly+asymptotically+stable+attractor+for+the+ODE+implies+the+existence+of+a+beliefs+attractor%2C+to+which+the+learning+process+converges.+We+prove+almost+sure+convergence+by+assuming+that+agents+employ+a+projection+facility+and+convergence+with+positive+probability+dropping+this+assumption.+The+rise+of+a+limit+cycle+and+of+even+more+complex+attractors+is+established+in+some+monetary+economics+models+assuming+that+agents+update+their+beliefs+with+the+Recursive+Ordinary+Least+Squares+and+the+Least+Mean+Squares+algorithm.&rft.publisher=WP-96-046&rft.date=1996-05&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4980%2F1%2FWP-96-046.pdf&rft.identifier=++Barucci%2C+E.+%26+Posch%2C+M.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F1515.html%3E++(1996).++The+Rise+of+Complex+Beliefs+Dynamics.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-96-046+++++