The criterion for uniqueness of quasi-stationary distributions of Markov processes and their domain of attraction problem

2014/10/07 by Hanjun Zhang, Zhang, Hanjun, Pengwen Guo +3
Mathematics · #60J27 (Primary) 60J80(Secondary) #FOS: Mathematics #Graph theory and applications #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Probability (math.PR) #math.PR #msc:60J27

paper · pdf · doi:10.48550/arxiv.1410.1638

This paper has been withdrawn by the authors due to a result contain mistakes

openalex publication_date 2014/10/07 · arxiv created 2014/10/08 · arxiv updated 2014/10/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider a Markov process X(t) on the nonnegative integers E= S ∪ \0\, where S=\1,2,...\ is an irreducible class and 0 is an absorbing state. In this paper, we investigate conditions under which the quasi-stationary distribution for X(t) exists and is unique, and any initial distribution supported in S is in the domain of attraction of this quasi-stationary distribution. We further find five conditions which are equivalent to that the extinction time is uniformly bounded. As a consequence, we prove the van Doorn's conjecture in \citeVD2012. And we can greatly improve theorem 1 in \citeVD2012.

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