?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%2F4466%2F&rft.title=Non-Standard+Limit+Theorems+for+Urn+Models+and+Stochastic+Approximation+Procedures&rft.creator=Kaniovski%2C+Y.M.&rft.creator=Pflug%2C+G.C.&rft.description=The+adaptive+processes+of+growth+modeled+by+a+generalized+urn+scheme+have+proved+to+be+an+efficient+tool+for+the+analysis+of+complex+phenomena+in+economics%2C+biology%2C+and+physical+chemistry.+They+demonstrate+non-ergodic+limit+behavior+with+multiple+limit+states.+There+are+two+major+sources+of+complex+feedbacks+governing+these+processes%3A+non-linearity+(even+local+which+is+caused+by+non-differentiability+of+the+functions+driving+them)+and+multiplicity+of+limit+states+stipulated+by+the+non-linearity.+The+authors+suggest+an+analytical+approach+for+studying+some+of+the+patterns+of+complex+limit+behavior.+The+approach+is+based+on+conditional+limit+theorems.+The+corresponding+limits+are%2C+in+general%2C+not+infinitely+divisible.+They+show+that+convergence+rates+could+vary+for+different+limit+states.+The+rates+depend+upon+the+smoothness+(in+neighborhoods+of+the+limit+states)+of+the+functions+governing+the+processes.+Since+the+mathematical+machinery+allows+us+to+treat+a+quite+general+class+of+recursive+stochastic+discrete-time+processes%2C+we+also+derive+corresponding+limit+theorems+for+stochastic+approximation+procedures.+The+theorems+yield+new+insight+into+the+limit+behavior+of+stochastic+approximation+procedures+in+the+case+of+non-differentiable+regression+functions+with+multiple+roots.&rft.publisher=RR-95-008.+Reprinted+from+Stochastic+Models%2C+11(1)%3A79-102+%5B1995%5D.&rft.date=1995&rft.type=Monograph&rft.type=PeerReviewed&rft.format=text&rft.language=en&rft.rights=cc_by&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4466%2F1%2FRR-95-08.pdf&rft.identifier=++Kaniovski%2C+Y.M.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F2009.html%3E+%26+Pflug%2C+G.C.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F229.html%3E+ORCID%3A+https%3A%2F%2Forcid.org%2F0000-0001-8215-3550+%3Chttps%3A%2F%2Forcid.org%2F0000-0001-8215-3550%3E++(1995).++Non-Standard+Limit+Theorems+for+Urn+Models+and+Stochastic+Approximation+Procedures.+++IIASA+Research+Report+(Reprint).+IIASA%2C+Laxenburg%2C+Austria%3A+RR-95-008.+Reprinted+from+Stochastic+Models%2C+11(1)%3A79-102+%5B1995%5D.+++++