eprintid: 4573 rev_number: 21 eprint_status: archive userid: 351 dir: disk0/00/00/45/73 datestamp: 2016-01-15 02:06:22 lastmod: 2021-08-27 17:15:23 status_changed: 2016-01-15 02:06:22 type: monograph metadata_visibility: show item_issues_count: 2 creators_name: Kaniovski, Y.M. creators_id: AL0815 title: Strong Convergence of Stochastic Approximation Without Lyapunov Functions ispublished: pub internal_subjects: iis_ecn internal_subjects: iis_met internal_subjects: iis_sys divisions: prog_ted abstract: We prove convergence with probability one of a multivariate Markov stochastic approximation procedure of the Robbins-Monro type with several roots. The argument exploits convergence of the corresponding system of ordinary differential equations to its stationary points. If the points are either linearly stable or linearly unstable, we prove convergence with probability 1 of the procedure to a random vector whose distribution concentrates on the set of stable stationary points. This generalizes for procedures with several roots the approach suggested by L. Ljung for processes with a single root. Along with stochastic approximation processes as such, the result can be applied to generalized urn schemes and stochastic models of technological and economic dynamics based on them, in particular, evolutionary games with incomplete information. date: 1995-02 date_type: published publisher: WP-95-019 iiasapubid: WP-95-019 price: 10 creators_browse_id: 2009 full_text_status: public monograph_type: working_paper place_of_pub: IIASA, Laxenburg, Austria pages: 12 coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/book citation: Kaniovski, Y.M. (1995). Strong Convergence of Stochastic Approximation Without Lyapunov Functions. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-95-019 document_url: https://pure.iiasa.ac.at/id/eprint/4573/1/WP-95-019.pdf