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A succesful method to describe the asymptotic behavior of a discrete timestochastic process governed by some recursive formula is to relate it to thelimit sets of a well chosen mean differential equation. Under an attainabilitycondition, convergence to a given attractor of the flow induced by thisdynamical system was proved to occur with positive probability (Bena\"im, 1999)for a class of Robbins Monro algorithms. Bena\"im et al. (2005) generalisedthis approach for stochastic approximation algorithms whose average behavior isrelated to a differential inclusion instead. We pursue the analogy by extendingto this setting the result of convergence with positive probability to anattractor.

Stochastic approximations of set-valued dynamical systems: Convergence with positive probability to an attractor