Existence and uniqueness of a quasistationary distribution for Markov processes with fast return from infinity (Q2923434)

A quasi-stationary distribution (QSD) for a stable continuous-time Markov process evolving in the positive integer space \(X\) is a probability measure which is stationary for the process conditioned not to be absorbed. The contributions of the article are two-fold. Firstly one gives a criterion which warrants the existence and the uniqueness of a QSD, and secondly one shows that the conditional distribution of the considered process converges exponentially fast in the total variation norm to a unique QSD.