169 citations · 527 across the 30 of their papers we have counts for
26 papers · 1 filter
Selection principles for quasi-stationary distributions and reinforcement processes
Michel Benaïm, Tresnia Berah, Pierre Germain
Let be a sub-Markov matrix on a finite set , representing the transition probabilities of a Markov chain on \(S\) absorbed at a cemetery point . We conside…
Regularity of invariant densities for random switching between two linear odes in Rd
Michel Benaim, Améthyste Bichard
In a paper entitled singularities of invariant densities for random switching between two linear odes in 2D, Bakhtin et al [5], consider a Markov process obtained by random switchi…
The asymptotic behavior of fraudulent algorithms
Michel Benaïm, Laurent Miclo
Let be a Morse function on a compact connected -dimensional Riemannian manifold, satisfying and let be the s…
On invariant distributions of Feller Markov chains with applications to dynamical systems with random switching
Michel Benaïm, Oliver Tough
We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuou…
Regularity of the stationary density for systems with fast random switching
Michel Benaïm, 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 obtai…
Transcritical bifurcation for the conditional distribution of a diffusion process
Michel Benaïm, Nicolas Champagnat, William Oçafrain +1
In this article, we describe a simple class of models of absorbed diffusion processes with parameter, whose conditional law exhibits a transcritical bifurcation. Our proofs are bas…
Degenerate processes killed at the boundary of a domain
Michel Benaïm, Nicolas Champagnat, William Oçafrain +1
We investigate certain properties of degenerate Feller processes that are killed when exiting a relatively compact set. Our main result provides general conditions ensuring that su…
Stochastic persistence in degenerate stochastic Lotka-Volterra food chains
Michel Benaïm, Antoine Bourquin, Dang H. Nguyen
We consider a Lotka-Volterra food chain model with possibly intra-specific competition in a stochastic environment represented by stochastic differential equations. In the non-dege…
Stochastic Persistence
Michel Benaim
Let be a continuous time Markov process on some metric space leaving invariant a closed subset called the {\em extinction set}. We give gen…
Convergence analysis of Adaptive Biasing Potential methods for diffusion processes
Michel Benaïm, Charles-Edouard Bréhier
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adapti…
Random Switching between Vector Fields Having a Common Zero
Michel Benaïm, Edouard Strickler
Let be a finite set, a family of vector fields on leaving positively invariant a compact set and having a common zero We consi…
On strict convergence of stochastic gradients
Michel Benaim
We discuss conditions ensuring the (strict) convergence of stochastic gradient algorithms.
Ergodicity of inhomogeneous Markov chains through asymptotic pseudotrajectories
Michel Benaïm, Florian Bouguet, Bertrand Cloez
In this work, we consider an inhomogeneous (discrete time) Markov chain and are interested in its long time behavior. We provide sufficient conditions to ensure that some of its as…
Self-repelling diffusions on a Riemannian manifold
Michel Benaïm, Carl-Erik Gauthier
Let M be a compact connected oriented Riemannian manifold. The purpose of this paper is to investigate the long time behavior of a degenerate stochastic differential equation on th…
Lotka Volterra in fluctuating environment or "how switching between beneficial environments can make survival harder"
Michel Benaïm, Claude Lobry
We consider two dimensional Lotka-Volterra systems in fluctuating environment. Relying on recent results on stochastic persistence and piecewise deterministic Markov processes, we…
Self-repelling diffusions via an infinite dimensional approach
Michel Benaim, Ioana Ciotir, Carl-Erik Gauthier
In the present work we study self-interacting diffusions following an infinite dimensional approach. First we prove existence and uniqueness of a solution with Markov property. The…
A stochastic approximation approach to quasi-stationary distributions on finite spaces
Michel Benaïm, Bertrand Cloez
This work is concerned with the analysis of a stochastic approximation algorithm for the simulation of quasi-stationary distributions on finite state spaces. This is a generalizati…
A generalized Pólya's Urn with graph based interactions: convergence at linearity
Jun Chen, Cyrille Lucas
We consider a special case of the generalized Pólya's urn model introduced by Benaim et al (2013). Given a finite connected graph , place a bin at each vertex. Two bins are call…
A generalized Polya's urn with graph based interactions
Michel Benaim, Itai Benjamini, Jun Chen +1
Given a finite connected graph G, place a bin at each vertex. Two bins are called a pair if they share an edge of G. At discrete times, a ball is added to each pair of bins. In a p…
Strongly Vertex-Reinforced-Random-Walk on the complete graph
Michel Benaïm, Olivier Raimond, Bruno Schapira
We study Vertex-Reinforced-Random-Walk on the complete graph with weights of the form , with . Unlike for the Edge-Reinforced-Random-Walk, which in this case localiz…
On the stability of planar randomly switched systems
Michel Benaïm, Stéphane Le Borgne, Florent Malrieu +1
Consider the random process (Xt) solution of dXt/dt = A(It) Xt where (It) is a Markov process on {0,1} and A0 and A1 are real Hurwitz matrices on R2. Assuming that there exists lam…
Qualitative properties of certain piecewise deterministic Markov processes
Michel Benaïm, Stéphane Le Borgne, Florent Malrieu +1
We study a class of Piecewise Deterministic Markov Processes with state space Rd x E where E is a finite set. The continuous component evolves according to a smooth vector field th…
Quantitative ergodicity for some switched dynamical systems
Michel Benaïm, Stéphane Le Borgne, Florent Malrieu +1
We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd \times E where E is a finite set. The continuou…
Consistency of vanishing smooth fictitious play
Michel Benaïm, Mathieu Faure
We discuss consistency of Vanishing Smooth Fictitious Play, a strategy in the context of game theory, which can be regarded as a smooth fictitious play procedure, where the smoothi…