General criteria for the study of quasi-stationarity

N Champagnat, D Villemonais - Electronic Journal of Probability, 2023 - projecteuclid.org
For Markov processes with absorption, we provide general criteria ensuring the existence
and the exponential non-uniform convergence in weighted total variation norm to a quasi …

A non‐conservative Harris ergodic theorem

V Bansaye, B Cloez, P Gabriel… - Journal of the London …, 2022 - Wiley Online Library
We consider non‐conservative positive semigroups and obtain necessary and sufficient
conditions for uniform exponential contraction in weighted total variation norm. This ensures …

Quasi-stationary distribution for strongly Feller Markov processes by Lyapunov functions and applications to hypoelliptic Hamiltonian systems

A Guillin, B Nectoux, L Wu - Journal of the European …, 2024 - content.ems.press
We establish a general result on the existence and uniqueness of a quasi-stationary
distribution D of a strongly Feller Markov process. Xt; t 0/killed when it exits a domain D …

A Lyapunov approach to stability of positive semigroups: An overview with illustrations

M Arnaudon, P Del Moral… - Stochastic Analysis and …, 2024 - Taylor & Francis
The stability analysis of possibly time varying positive semigroups on non-necessarily
compact state spaces, including Neumann and Dirichlet boundary conditions is a …

Degenerate processes killed at the boundary of a domain

M Benaïm, N Champagnat, W Oçafrain… - arxiv preprint arxiv …, 2021 - arxiv.org
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 such a …

Lyapunov criteria for uniform convergence of conditional distributions of absorbed Markov processes

N Champagnat, D Villemonais - Stochastic Processes and their …, 2021 - Elsevier
We study the uniform convergence to quasi-stationarity of multidimensional processes
absorbed when one of the coordinates vanishes. Our results cover competitive or weakly …

On the stability of positive semigroups

P Del Moral, E Horton, A Jasra - The Annals of Applied Probability, 2023 - projecteuclid.org
The stability and contraction properties of positive integral semigroups on Polish spaces are
investigated. Our novel analysis is based on the extension of V-norm contraction methods …

Long time behavior of killed Feynman-Kac semigroups with singular Schr {\" o} dinger potentials

A Guillin, DI Lu, B Nectoux, L Wu - arxiv preprint arxiv:2411.13099, 2024 - arxiv.org
In this work, we investigate the compactness and the long time behavior of killed Feynman-
Kac semigroups of various processes arising from statistical physics with very general …

Quasi-stationary distribution for Hamiltonian dynamics with singular potentials

A Guillin, B Nectoux, L Wu - Probability Theory and Related Fields, 2023 - Springer
Quasi-stationary distribution for Hamiltonian dynamics with singular potentials | Probability
Theory and Related Fields Skip to main content SpringerLink Account Menu Find a journal …

Unique quasi-stationary distribution, with a possibly stabilizing extinction

A Velleret - Stochastic Processes and their Applications, 2022 - Elsevier
We establish sufficient conditions for exponential convergence to a unique quasi-stationary
distribution in the total variation norm. These conditions also ensure the existence and …