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- W4301213501 abstract "We study the long time behaviour of a Markov process evolving in $mathbb{N}$ and conditioned not to hit 0. Assuming that the process comes back quickly from infinity, we prove that the process admits a unique quasi-stationary distribution (in particular, the distribution of the conditioned process admits a limit when time goes to infinity). Moreover, we prove that the distribution of the process converges exponentially fast in total variation norm to its quasi-stationary distribution and we provide an explicit rate of convergence. As a first application of our result, we bring a new insight on the speed of convergence to the quasi-stationary distribution for birth and death processes: we prove that these processes converge exponentially fast to a quasi-stationary distribution if and only if they have a unique quasi-stationary distribution. Also, considering the lack of results on quasi-stationary distributions for non-irreducible processes on countable spaces, we show, as a second application of our result, the existence and uniqueness of a quasi-stationary distribution for a class of possibly non-irreducible processes." @default.
- W4301213501 created "2022-10-05" @default.
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- W4301213501 date "2012-02-03" @default.
- W4301213501 modified "2023-10-18" @default.
- W4301213501 title "Existence and uniqueness of a quasi-stationary distribution for Markov processes with fast return from infinity" @default.
- W4301213501 doi "https://doi.org/10.48550/arxiv.1202.0677" @default.
- W4301213501 hasPublicationYear "2012" @default.
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