General criteria for the study of quasi-stationarity

2017/12/21 by Nicolas Champagnat, Champagnat, Nicolas, Denis Villemonais +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · #37A25 #60B10 #60F99 #60J05 #60J10 #60J25 #60J27 (Primary) 60J60 #60J75 #60J80 #93E03 (Secondary) #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1712.08092

openalex publication_date 2017/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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