General criteria for the study of quasi-stationarity

Nicolas Champagnat 1, 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 : 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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  • HAL Id : hal-01672979, version 2
  • ARXIV : 1712.08092

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Nicolas Champagnat, Denis Villemonais. General criteria for the study of quasi-stationarity. 2017. ⟨hal-01672979v2⟩

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