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Benaim, Michel
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Benaim, Michel
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Professeur ordinaire
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michel.benaim@unine.ch
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Voici les éléments 1 - 10 sur 10
- PublicationAccès libreStrongly reinforced vertex-reinforced-random-walk on the complete graph(2012)
; ;Raimond, OlivierSchapira, Bruno - PublicationAccès libreSelf-interacting diffusions IV: Rate of convergence(2011)
; Raimond, Olivier - PublicationMétadonnées seulementA class of self-interacting processes with applications to games and reinforced random walks(2010)
; Raimond, Olivier - PublicationAccès libreA Bakry-Emery Criterion for self-interacting diffusions(2007)
; Raimond, Olivier - PublicationMétadonnées seulementA Bakry-Emery criterion for self-interacting diffusions(: Birkhauser Boston, 2005)
; ;Raimond, Olivier ;Dalang, Marco ;Dozzi, MarcoRusso, FrancescoWe give a Bakry-Emery type criterion for self-interacting diffusions on a compact manifold. - PublicationAccès libreSelf-interacting diffusions. III. Symmetric interactions(2005)
; Raimond, OlivierLet M be a compact Riemannian manifold. A self-interacting diffusion on M is a stochastic process solution to where {W-t} is a Brownian vector field on M and V-x(y) = V(x, y) a smooth function. Let mu(t) = 1/t integral(0)(t) delta X-s ds denote the normalized occupation measure of X-t. We prove that, when V is symmetric, mu(t) converges almost surely to the critical set of a certain nonlinear free energy functional J. Furthermore, J has generically finitely many critical points and mu(t) converges almost surely toward a local minimum of J. Each local minimum has a positive probability to be selected. - PublicationAccès libreSelf-interacting diffusions II: Convergence in law(2003)
; Raimond, OlivierThis paper concerns convergence in law properties of self-interacting diffusions on a compact Riemannian manifold. (C) 2003 Editions scientifiques et medicales Elsevier SAS. - PublicationAccès libreSelf-interacting diffusions(2002)
; ;Ledoux, MichelRaimond, OlivierThis paper is concerned with a general class of self-interacting diffusions [X-t}(tgreater than or equal to0) living oil a compact Riemannian manifold M. These are solutions to stochastic differential equations of the form : dX(t) = Brownian increments + drift term depending on X-t and mu(t), the normalized occupation measure of the process. It is proved that the asymptotic behavior of {mu(t)} can be precisely related to the asymptotic behavior of a deterministic dynamical semi-flow Phi = {Phi(t)}(tgreater than or equal to0) defined on the space of the Borel probability measures on M. In particular, the limit sets of {mu(t)} are proved to be almost surely attractor free sets for Phi. These results are applied to several examples of self-attracting/repelling diffusions on the n-sphere. For instance, in the case of self-attracting diffusions, our results apply to prove that {mu(t)} can either converge toward the normalized Riemannian measure, or to a gaussian measure, depending on the value of a parameter measuring the strength of the attraction. - PublicationAccès libreOnself attracting/repelling diffusions(2002)
; Raimond, OlivierWe present an almost sure ergodic theorem for a class of self-interacting diffusions on a compact Riemannian manifold. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS. - PublicationMétadonnées seulement