eprintid: 4270 rev_number: 8 eprint_status: archive userid: 351 dir: disk0/00/00/42/70 datestamp: 2016-01-15 02:05:07 lastmod: 2021-08-27 17:15:03 status_changed: 2016-01-15 02:05:07 type: article metadata_visibility: show item_issues_count: 2 creators_name: Kaniovski, Y.M. creators_name: Pflug, G.C. creators_id: AL0815 creators_id: 1361 creators_orcid: 0000-0001-8215-3550 title: Non-standard limit theorems for urn models and stochastic approximation procedures ispublished: pub internal_subjects: iis_met internal_subjects: iis_mod internal_subjects: iis_ecn divisions: prog_opt divisions: prog_ted keywords: generalized urn scheme, conditional limit theorems, stochastic approximation abstract: 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, biology and physical chemistry. They demonstrate non-ergodic limit behavior with multiple limit states. There are two major sources of complex feedbacks governing these processes: nonlinearity (even local, which is caused by nondifferentiability of the functions driving them) and multiplicity of limit states stipulated by the nonlinearity.We 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, in general, not infinitely divisible. We show that convergence rates could be different 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, 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 nondifferentiable regression functions with multiple roots date: 1995 date_type: published publisher: Taylor & Francis id_number: 10.1080/15326349508807332 iiasapubid: XJ-95-063 iiasa_bibref: Stochastic Models; 11(1):79-102 [1995] iiasa_bibnotes: Available as IIASA Reprint RP-95-008 creators_browse_id: 2009 creators_browse_id: 229 full_text_status: none publication: Stochastic Models volume: 11 number: 1 pagerange: 79-102 refereed: TRUE issn: 1532-4214 coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/article citation: Kaniovski, Y.M. & Pflug, G.C. ORCID: https://orcid.org/0000-0001-8215-3550 (1995). Non-standard limit theorems for urn models and stochastic approximation procedures. Stochastic Models 11 (1) 79-102. 10.1080/15326349508807332 .