Stochastic Approximations of Set-Valued Dynamical Systems: Convergence with Positive Probability to an Attractor

Mathieu Faure, Gregory Roth
2010 Mathematics of Operations Research  
A succesful 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, convergence to a given attractor of the flow induced by this dynamical system was proved to occur with positive probability (Bena\"im, 1999) for a class of Robbins Monro algorithms. Bena\"im et al. (2005) generalised this approach for stochastic
more » ... 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.
doi:10.1287/moor.1100.0455 fatcat:gh2ewr2xc5ccdn4d7p7cnlgjou