71 citations · 303 across the 42 of their papers we have counts for
42 papers · 1 filter
From stochastic individual-based models to free-boundary Hamilton-Jacobi equations
Nicolas Champagnat, Sylvie Méléard, Sepideh Mirrahimi +1
We study a stochastic branching model for a population structured by a quantitative phenotypic trait and subject to births, deaths, and mutations. In a regime of large population a…
Quasi-stationary distribution for kinetic SDEs with low regularity coefficients
Nicolas Champagnat, Tony Lelièvre, Mouad Ramil +2
We consider kinetic SDEs with low regularity coefficients in the setting recently introduced in [6]. For the solutions to such equations, we first prove a Harnack inequality. Using…
Uniform Wasserstein convergence of penalized Markov processes
Nicolas Champagnat, Edouard Strickler, Denis Villemonais
For general penalized Markov processes with soft killing, we propose a simple criterion ensuring uniform convergence of conditional distributions in Wasserstein distance to a uniqu…
Convergence of population processes with small and frequent mutations to the canonical equation of adaptive dynamics
Nicolas Champagnat, Vincent Hass
In this article, a stochastic individual-based model describing Darwinian evolution of asexual, phenotypic trait-structured population, is studied. We consider a large population w…
Quasi-limiting estimates for periodic absorbed Markov chains
Nicolas Champagnat, Denis Villemonais
We consider periodic Markov chains with absorption. Applying to iterates of this periodic Markov chain criteria for the exponential convergence of conditional distributions of aper…
Filling the gap between individual-based evolutionary models and Hamilton-Jacobi equations
Nicolas Champagnat, Sylvie Méléard, Sepideh Mirrahimi +1
We consider a stochastic model for the evolution of a discrete population structured by a trait with values on a finite grid of the torus, and with mutation and selection. Traits a…
Existence, uniqueness and ergodicity for the centered Fleming-Viot process
Nicolas Champagnat, Vincent Hass
Motivated by questions of ergodicity for shift invariant Fleming-Viot process, we consider the centered Fleming-Viot process defined by $Z_{t}…
Quasi-stationary distributions in reducible state spaces
Nicolas Champagnat, Denis Villemonais
We study quasi-stationary distributions and quasi-limiting behavior of Markov chains in general reducible state spaces with absorption. We propose a set of assumptions dealing with…
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 approximation of quasi-stationary distributions for diffusion processes in a bounded domain
Michel Benaïm, Nicolas Champagnat, Denis Villemonais
We study a random process with reinforcement, which evolves following the dynamics of a given diffusion process in a bounded domain and is resampled according to its occupation mea…
Practical criteria for R-positive recurrence of unbounded semigroups
Nicolas Champagnat, Denis Villemonais
The goal of this note is to show how recent results on the theory of quasi-stationary distributions allow to deduce effortlessly general criteria for the geometric convergence of n…
Stochastic analysis of emergence of evolutionary cyclic behavior in population dynamics with transfer
Nicolas Champagnat, Sylvie Méléard, Viet Chi Tran
Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be…
Convergence of the Fleming-Viot process toward the minimal quasi-stationary distribution
Nicolas Champagnat, Denis Villemonais
We prove under mild conditions that the Fleming-Viot process selects the minimal quasi-stationary distribution for Markov processes with soft killing on non-compact state spaces. O…
Probabilistic Non-asymptotic Analysis of Distributed Algorithms
Nicolas Champagnat, René Schott, Denis Villemonais
We present a new probabilistic analysis of distributed algorithms. Our approach relies on the theory of quasi-stationary distributions (QSD) recently developped by Champagnat and V…
General criteria for the study of quasi-stationarity
Nicolas Champagnat, Denis Villemonais
For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary d…
A probabilistic approach to Dirac concentration in nonlocal models of adaptation with several resources
Nicolas Champagnat, Benoît Henry
This work is devoted to the study of scaling limits in small mutations and large time of the solutions u^ of two deterministic models of phenotypic adaptation, where the paramet…
Lyapunov criteria for uniform convergence of conditional distributions of absorbed Markov processes
Nicolas Champagnat, Denis Villemonais
We study the quasi-stationary behavior of multidimensional processes absorbed when one of the coordinates vanishes. Our results cover competitive or weakly cooperative Lotka-Volter…
Population processes with unbounded extinction rate conditioned to non-extinction
Nicolas Champagnat, Denis Villemonais
This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes an…
Uniform convergence to the Q-process
Nicolas Champagnat, Denis Villemonais
The first aim of the present note is to quantify the speed of convergence of a conditioned process toward its Q-process under suitable assumptions on the quasi-stationary distribut…
On the link between infinite horizon control and quasi-stationary distributions
Julien Claisse, Nicolas Champagnat
We study infinite horizon control of continuous-time non-linear branching processes with almost sure extinction for general (positive or negative) discount. Our main goal is to stu…
Uniform convergence of penalized time-inhomogeneous Markov processes
Nicolas Champagnat, Denis Villemonais
We provide an original and general sufficient criterion ensuring the exponential contraction of Feynman-Kac semi-groups of penalized processes. This criterion is applied to time-in…
Criteria for exponential convergence to quasi-stationary distributions and applications to multi-dimensional diffusions
Nicolas Champagnat, Koléhè Coulibaly-Pasquier, Denis Villemonais
We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not…
Exponential convergence to quasi-stationary distribution for absorbed one-dimensional diffusions with killing
Nicolas Champagnat, Denis Villemonais
This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusion processes with killing on . We obtain criteria for the exponential convergence…