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

@article{Faure2010StochasticAO, title={Stochastic Approximations of Set-Valued Dynamical Systems: Convergence with Positive Probability to an Attractor}, author={Mathieu Faure and Gregory Roth}, journal={Math. Oper. Res.}, year={2010}, volume={35}, pages={624-640} }

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…

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