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arXiv · 1712.08092

General criteria for the study of quasi-stationarity

Nicolas Champagnat·Denis Villemonais
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Abstract

For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of attraction by an integrability condition, prove the existence of a right eigenvector for the semigroup of the process and the existence and exponential ergodicity of the Q-process. These results are applied to one-dimensional and multi-dimensional diffusion processes, to pure jump continuous time processes, to reducible processes with several communication classes, to perturbed dynamical systems and discrete time processes evolving in discrete state spaces.

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Nicolas Champagnat, Denis Villemonais. 2017-12-21. General criteria for the study of quasi-stationarity. https://arxiv.org/abs/1712.08092

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