Stochastic Approximations of Set-Valued Dynamical Systems: Convergence with Positive Probability to an Attractor
成果类型：
Article
署名作者：
Faure, Mathieu; Roth, Gregory
署名单位：
University of Neuchatel
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.1100.0455
发表日期：
2010
页码：
624-640
关键词：
摘要：
A successful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well-chosen mean differential equation. Under an attainability condition, Benaim proved that convergence to a given attractor of the flow induced by this dynamical system occurs with positive probability for a class of Robbins Monro algorithms. Benaim, Hofbauer, and Sorin generalised this approach for stochastic approximation algorithms whose average behavior is related to a differential inclusion instead. We pursue the analogy by extending to this setting the result of convergence with positive probability to an attractor.
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