Time to Absorption in Markov Chains as a Mixture Distribution of Hypo-Exponential Distributions

Hiller Josh ()
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Hiller Josh: Department of Mathematics and Computer Science, Adelphi University, Garden City, NY 11530, USA

Stochastics and Quality Control, 2023, vol. 38, issue 2, 119-123

Abstract: We given an elementary proof that in a Markov chain with absorbing states, and positive probability of absorption at some time t > 0 {t>0} , time to absorption follows a mixture distribution of hypo-exponential random variables. We use this fact to show that early approximations of such a distribution yield the length of the shortest path from an initial state to an absorbing state. Thus different Markov chains with the same distance of shortest paths can yield identical first order approximations. Our work is motivated by the classical Armitage and Doll model of carcinogenesis.

Keywords: Markov Chains; Carcinogenesis; Mixing Distribution (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1515/eqc-2023-0028

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