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Journal articles
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.
https://hal.archives-ouvertes.fr/hal-01209975
Contributor : Archive Ouverte Prodinra <>
Submitted on : Friday, October 2, 2015 - 10:22:09 PM
Last modification on : Monday, July 6, 2020 - 3:39:59 PM
Contributor : Archive Ouverte Prodinra <>
Submitted on : Friday, October 2, 2015 - 10:22:09 PM
Last modification on : Monday, July 6, 2020 - 3:39:59 PM