191 citations · 256 across the 29 of their papers we have counts for
39 papers
Averaging principle for jump processes depending on fast ergodic dynamics
Vincent Kagan, Edouard Strickler, Denis Villemonais
We consider a slow-fast stochastic process where the slow component is a jump process on a measurable index set whose transition rates depend on the position of the fast component.…
Quasi-compactness for dominated kernels with application to quasi-stationary distribution theory
Denis Villemonais
We establish a domination principle for positive operators, which provides an upper bound on the essential spectral radius and yields quasi-compactness criteria on weighted supremu…
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…
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…
Binary branching processes with Moran type interactions
Alexander M. G. Cox, Emma Horton, Denis Villemonais
The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, re…
The Multi-type Bisexual Galton-Watson Branching Process
Coralie Fritsch, Denis Villemonais, Nicolás Zalduendo
In this work we study the bisexual Galton-Watson process with a finite number of types, where females and males mate according to a ''mating function'' and form couples of differen…
General diffusion processes as the limit of time-space Markov chains
Alexis Anagnostakis, Antoine Lejay, Denis Villemonais
We prove the convergence of the law of grid-valued random walks, which can be seen as time-space Markov chains, to the law of a general diffusion process. This includes processes w…
A quasi-stationary approach to the long-term asymptotics of the growth-fragmentation equation
Denis Villemonais, Alexander Watson
In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the…
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…
Fluctuations of balanced urns with infinitely many colours
Svante Janson, Cécile Mailler, Denis Villemonais
In this paper, we prove convergence and fluctuation results for measure-valued Pólya processes (MVPPs, also known as Pólya urns with infinitely-many colours). Our convergence resul…
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…
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…
Stochastic Methods for the Neutron Transport Equation I: Linear Semigroup asymptotics
Emma Horton, Andreas E. Kyprianou, Denis Villemonais
The Neutron Transport Equation (NTE) describes the flux of neutrons through an inhomogeneous fissile medium. In this paper, we reconnect the NTE to the physical model of the spatia…
Stochastic approximation on non-compact measure spaces and application to measure-valued Pólya processes
Cécile Mailler, Denis Villemonais
Our main result is to prove almost-sure convergence of a stochastic-approximation algorithm defined on the space of measures on a non-compact space. Our motivation is to apply this…
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…
Lower bound for the coarse Ricci curvature of continuous-time pure jump processes
Denis Villemonais
We obtain a lower bound for the coarse Ricci curvature of continuous time pure jump Markov processes, with an emphasis on interacting particle systems. Applications to several mode…
Perpetual integrals convergence and extinctions in population dynamics
Camille Coron, Sylvie Méléard, Denis Villemonais
In this article we use a criterion for the integrability of paths of one-dimensional diffusion processes from which we derive new insights on allelic fixation in several situations…
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…