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Criteria for Exponential Convergence to Quasi-Stationary Distributions and Applications to Multi-Dimensional Diffusions

  • Nicolas Champagnat
  • Koléhè Abdoulaye Coulibaly-Pasquier
  • Denis Villemonais
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2215)

Abstract

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 \(\mathbb {R}^d\) or in compact Riemannian manifolds with boundary, with absorption at the boundary.

Keywords

Markov processes Diffusions in Riemannian manifolds Diffusions in bounded domains Absorption at the boundary Quasi-stationary distributions Q-process Uniform exponential mixing Two-sided estimates Gradient estimates 

2010 Mathematics Subject Classification

Primary: 60J60 37A25 60B10 60F99 Secondary: 60J75 60J70 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Nicolas Champagnat
    • 1
    • 2
    • 3
  • Koléhè Abdoulaye Coulibaly-Pasquier
    • 1
    • 2
    • 3
  • Denis Villemonais
    • 1
    • 2
    • 3
  1. 1.Université de Lorraine, IECL, UMR 7502Vandœuvre-lès-NancyFrance
  2. 2.CNRS, IECL, UMR 7502Vandœuvre-lès-NancyFrance
  3. 3.InriaVillers-lès-NancyFrance

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