Exponentiality of First Passage Times of Continuous Time Markov Chains

Abstract : Let 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 relative to T, then this time is exponentially distributed under . 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 . 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.
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Romain Bourget, Loic Chaumont, Natalia Sapoukhina. Exponentiality of First Passage Times of Continuous Time Markov Chains. Acta Applicandae Mathematicae, Springer Verlag, 2014, 131 (1), pp.197-212. 〈10.1007/s10440-013-9854-z〉. 〈hal-01209975〉



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