Strong Convergence of Stochastic Approximation Without Lyapunov Functions

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/4127 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/4127 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/4127 archive 351 disk0/00/00/45/73 2016-01-15 02:06:22 2021-08-27 17:15:23 2016-01-15 02:06:22 monograph show 2 Kaniovski Y.M. AL0815 Strong Convergence of Stochastic Approximation Without Lyapunov Functions pub iis_ecn iis_met iis_sys prog_ted 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. 1995-02 published WP-95-019 WP-95-019 10 2009 public working_paper IIASA, Laxenburg, Austria 12 FALSE info:eu-repo/semantics/book