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Benaim, Michel
Nom
Benaim, Michel
Affiliation principale
Fonction
Professeur ordinaire
Email
michel.benaim@unine.ch
Identifiants
Résultat de la recherche
Voici les éléments 1 - 10 sur 10
- PublicationAccès libreOn invariant distributions of Feller Markov chains with applications to dynamical systems with random switching(2023-10-26T16:39:02Z)
; Oliver ToughWe introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the Riemannian measure. This is applied to Markov chains obtained by random composition of maps and to piecewise deterministic Markov processes obtained by random switching between flows. - PublicationAccès libreA note on the top Lyapunov exponent of linear cooperative systems(2023-02-12T08:49:27Z)
; - PublicationAccès libreRegularity of the stationary density for systems with fast random switching(2022-12-07T13:41:53Z)
; Oliver ToughWe 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. - PublicationAccès libreDegenerate processes killed at the boundary of a domain(2021-03-15T16:56:53Z)
; - PublicationAccès libreStochastic persistence in degenerate stochastic Lotka-Volterra food chains(2020-12-02T13:55:41Z)
; ; Dang H. NguyenWe consider a Lotka-Volterra food chain model with possibly intra-specific competition in a stochastic environment represented by stochastic differential equations. In the non-degenerate setting, this model has already been studied by A. Hening and D. Nguyen. They provided conditions for stochastic persistence and extinction. In this paper, we extend their results to the degenerate situation in which the top or the bottom species is subject to random perturbations. Under the persistence condition, there exists a unique invariant probability measure supported by the interior of $\mathbb{R}_+^n$ having a smooth density. Moreover, we study a more general model, in which we give new conditions which make it possible to characterise the convergence of the semi-group towards the unique invariant probability measure either at an exponential rate or at a polynomial one. This will be used in the stochastic Lotka-Volterra food chain to see that if intra-specific competition occurs for all species, the rate of convergence is exponential while in the other cases it is polynomial. - PublicationAccès libreOn strict convergence of stochastic gradients(2016-10-11T11:24:48Z)We discuss conditions ensuring the (strict) convergence of stochastic gradient algorithms.
- PublicationAccès libreSupports of Invariant Measures for Piecewise Deterministic Markov Processes(2016-04-21T09:01:47Z)
; - PublicationAccès libreSmale Strategies for Network Prisoner's Dilemma Games(2015-03-29T19:10:46Z)
; Morris W. HirschSmale'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. - PublicationAccès libreOn Gradient like Properties of Population games, Learning models and Self Reinforced Processes(2014-09-14T19:05:06Z)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.
- PublicationAccès libreStrongly Vertex-Reinforced-Random-Walk on the complete graph(2012-08-31T06:07:51Z)
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