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Applications of the fundamental matrix to mean absorption and conditional mean absorption problems

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  • Milliken, Evan

Abstract

A proof of a general theorem for the calculation of conditional mean duration of a finite absorbing discrete time Markov chain is presented. In the simplest case, this result is equivalent to one suggested in the book of Kemeny and Snell (1976). In addition, we prove that the mean duration and mean conditional duration of a finite absorbing continuous time Markov chain can be calculated via the fundamental matrix of the embedded discrete time chain. These results are also extended to certain non-absorbing Markov chains. Applications are presented to illustrate the utility of these results.

Suggested Citation

  • Milliken, Evan, 2019. "Applications of the fundamental matrix to mean absorption and conditional mean absorption problems," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 106-115.
    • Handle: RePEc:eee:stapro:v:151:y:2019:i:c:p:106-115
    DOI: 10.1016/j.spl.2019.04.001
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    1. Dey, Agnish & Mukherjea, Arunava, 2014. "Collapsing of non-homogeneous Markov chains," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 140-148.
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