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
- Quasi-stationary distributions
- diffusions in bounded domains
- diffusions in Riemannian manifolds
- Q-process
- two-sided estimates
- absorption at the boundary
- diffusions in a bounded domain
- Diffusions on Riemannian manifolds
- quasi-stationary distribution
- Markov processes
- gradient estimates
- uniform exponential mixing
Domaines
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