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- W4310652568 abstract "Let $(X,p_x)$ be a continuous time Markov chain with finite or countable state space $S$ and let $T$ be its first passage time in a subset $D$ of $S$. It is well known that if $mu$ is a quasi-stationary distribution relatively to $T$, then this time is exponentially distributed under $p_mu$. However, quasi-stationarity is not a necessary condition. In this paper, we determine more general conditions on an initial distribution $mu$ for $T$ to be exponentially distributed under $p_mu$. We show in addition how quasi-stationary distributions can be expressed in terms of any initial law which makes the distribution of $T$ exponential. We also study two examples in branching processes where exponentiality does imply quasi-stationarity." @default.
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- W4310652568 date "2012-11-15" @default.
- W4310652568 modified "2023-10-16" @default.
- W4310652568 title "Exponentiality of first passage times of continuous time Markov chains" @default.
- W4310652568 hasPublicationYear "2012" @default.
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