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

Nicolas Champagnat 1, 2 Abdoulaye Coulibaly-Pasquier 2 Denis Villemonais 1, 2
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : 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.
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Nicolas Champagnat, Abdoulaye Coulibaly-Pasquier, Denis Villemonais. Exponential convergence to quasi-stationary distribution for multi-dimensional diffusion processes. journal-article. 2016. 〈hal-01795090〉

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