Criteria for exponential convergence to quasi-stationary distributions and applications to multi-dimensional diffusions
Résumé
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 to be absorbed. The first one is based on two-sided estimates on the transition kernel of the process and the second one on gradient estimates on its semigroup. We apply these criteria to multi-dimensional diffusion processes in bounded domains of $\R^d$ or in compact Riemannian manifolds with boundary, with absorption at the boundary.
Mots clés
uniform exponential mixing
gradient estimates
Markov processes
quasi-stationary distribution
Diffusions on Riemannian manifolds
diffusions in a bounded domain
absorption at the boundary
two-sided estimates
Q-process
diffusions in Riemannian manifolds
diffusions in bounded domains
Quasi-stationary distributions
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
Loading...