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Journal Articles Electronic Journal of Probability Year : 2023

General criteria for the study of quasi-stationarity


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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Dates and versions

hal-01672979 , version 1 (28-12-2017)
hal-01672979 , version 2 (26-01-2018)
hal-01672979 , version 3 (21-10-2022)





Nicolas Champagnat, Denis Villemonais. General criteria for the study of quasi-stationarity. Electronic Journal of Probability, inPress. ⟨hal-01672979v3⟩
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