6 papers
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…
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-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…
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…
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…
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…