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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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  • Publication
    Accès libre
    A note on the top Lyapunov exponent of linear cooperative systems
    (2023-02-12T08:49:27Z)
    Benaim, Michel 
    ;
    Claude Lobry
    ;
    Tewfik Sari
    ;
    Strickler, Edouard 
    In a recent paper [Asymptotic of the largest Floquet multiplier for cooperative matrices Annales de la Facult\'e des Sciences de Toulouse, Tome XXXI, no 4 (2022)] P. Carmona gives an asymptotic formulae for the top Lyapunov exponent of a linear T-periodic cooperative differential equation, in the limit T goes to infinity. This short note discusses and extends this result.
  • Publication
    Accès libre
    Regularity of the stationary density for systems with fast random switching
    (2022-12-07T13:41:53Z)
    Benaim, Michel 
    ;
    Oliver Tough
    We consider the piecewise-deterministic Markov process obtained by randomly switching between the flows generated by a finite set of smooth vector fields on a compact set. We obtain H\"ormander-type conditions on the vector fields guaranteeing that the stationary density is: $C^k$ whenever the jump rates are sufficiently fast, for any $k<\infty$; unbounded whenever the jump rates are sufficiently slow and lower semi-continuous regardless of the jump rates. Our proofs are probabilistic, relying on a novel application of stopping times.
  • Publication
    Accès libre
    On strict convergence of stochastic gradients
    (2016-10-11T11:24:48Z)
    Benaim, Michel 
    We discuss conditions ensuring the (strict) convergence of stochastic gradient algorithms.
  • Publication
    Accès libre
    Supports of Invariant Measures for Piecewise Deterministic Markov Processes
    (2016-04-21T09:01:47Z)
    Benaim, Michel 
    ;
    Fritz Colonius
    ;
    Ralph Lettau
    For a class of piecewise deterministic Markov processes, the supports of the invariant measures are characterized. This is based on the analysis of controllability properties of an associated deterministic control system. Its invariant control sets determine the supports.
  • Publication
    Accès libre
    Smale Strategies for Network Prisoner's Dilemma Games
    (2015-03-29T19:10:46Z)
    Kashi Behrstock
    ;
    Benaim, Michel 
    ;
    Morris W. Hirsch
    Smale's approach to the classical two-players repeated Prisoner's Dilemma game is revisited here for N -players and Network games in the framework of Blackwell's approachability, stochastic approximations and differential inclusions.
  • Publication
    Accès libre
    On Gradient like Properties of Population games, Learning models and Self Reinforced Processes
    (2014-09-14T19:05:06Z)
    Benaim, Michel 
    We consider ordinary differential equations on the unit simplex of $\RR^n$ that naturally occur in population games, models of learning and self reinforced random processes. Generalizing and relying on an idea introduced in \cite{DF11}, we provide conditions ensuring that these dynamics are gradient like and satisfy a suitable "angle condition". This is used to prove that omega limit sets and chain transitive sets (under certain smoothness assumptions) consist of equilibria; and that, in the real analytic case, every trajectory converges toward an equilibrium. In the reversible case, the dynamics are shown to be $C^1$ close to a gradient vector field. Properties of equilibria -with a special emphasis on potential games - and structural stability questions are also considered.