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Benaim, Michel

Nom
Benaim, Michel
Affiliation principale
Fonction
Professeur ordinaire
Email
michel.benaim@unine.ch
Identifiants
https://libra.unine.ch/handle/123456789/457
_
0000-0003-0703-3107

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Filtres

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3
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  • Publication
    Accès libre
    Stochastic approximations and differential inclusions
    (2005)
    Benaim, Michel 
    ;
    Hofbauer, Josef
    ;
    Sorin, Sylvain
    The dynamical systems approach to stochastic approximation is generalized to the case where the mean differential equation is replaced by a differential inclusion. The limit set theorem of Benaim and Hirsch is extended to this situation. Internally chain transitive sets and attractors are studied in detail for set-valued dynamical systems. Applications to game theory are given, in particular to Blackwell's approachability theorem and the convergence of fictitious play.
  • Publication
    Accès libre
    Stochastic approximation algorithms with constant step size whose average is cooperative
    (1999)
    Benaim, Michel 
    ;
    Hirsch, Morris W
    We consider stochastic approximation algorithms with constant step size whose average ordinary differential equation (ODE) is cooperative and irreducible. We show that, under mild conditions on the noise process, invariant measures and empirical occupations measures of the process weakly converge (as the time goes to infinity and the step size goes to zero) toward measures which are supported by stable equilibria of the ODE. These results are applied to analyzing the long-term behavior of a class of learning processes arising in game theory.
  • Publication
    Accès libre
    On invariant hypersurfaces of strongly monotone maps
    (1997)
    Benaim, Michel 
    For C-k, k>1, strongly monotone discrete-time dynamical systems, we present simple criteria which ensure that nonmonotone invariant manifolds are C-k. (C) 1997 Academic Press.