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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