Exponential convergence to quasi-stationary distribution for multi-dimensional diffusion processes

Nicolas Champagnat (1, 2) , Abdoulaye Coulibaly-Pasquier (1) , Denis Villemonais (1, 2)

1 Probabilités et statistiques
2 TOSCA - TO Simulate and CAlibrate stochastic models

We consider diffusion processes killed at the boundary of Riemannian manifolds. The aim of the paper if to provide two different sets of assumptions ensuring the exponential convergence in total variation norm of the distribution of the process conditioned not to be killed. Our first criterion makes use of two sided estimates and applies to general Markov processes. Our second criterion is based on gradient estimates for the semi-group of diffusion processes.

Mots clés: Diffusions on Riemannian manifolds; diffusions in a bounded domain; absorption at the boundary; quasi-stationary distribution; Q-process; uniform exponential mixing; two-sided estimates; gradient estimates

Domaines: Probabilités [math.PR]

Nicolas Champagnat, Abdoulaye Coulibaly-Pasquier, Denis Villemonais. Exponential convergence to quasi-stationary distribution for multi-dimensional diffusion processes. 2016. ⟨hal-01293622v1⟩