Phase-type distributions and the structure of finite Markov chains

Robert S. Maier

doi:10.1016/0377-0427(93)90040-I

Phase-type distributions and the structure of finite Markov chains

Robert S. Maier

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

Maier, R.S., Phase-type distributions and the structure of finite Markov chains, Journal of Computational and Applied Mathematics 46 (1993) 449-453. We show that all discrete phase-type distributions arise as first passage times (i.e., absorption times) in finite-state Markov chains with a certain recursive internal structure. This arises from the special properties of an automata-theoretic algorithm which can be used to solve the inverse problem for phase-type distributions: the construction of a Markov chain with specified absorption time distribution.

Original language	English (US)
Pages (from-to)	449-453
Number of pages	5
Journal	Journal of Computational and Applied Mathematics
Volume	46
Issue number	3
DOIs	https://doi.org/10.1016/0377-0427(93)90040-I
State	Published - Jun 22 1993

Keywords

Markov chains
Phase-type distributions
first passage times
generating functions

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/0377-0427(93)90040-I

Cite this

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AB - Maier, R.S., Phase-type distributions and the structure of finite Markov chains, Journal of Computational and Applied Mathematics 46 (1993) 449-453. We show that all discrete phase-type distributions arise as first passage times (i.e., absorption times) in finite-state Markov chains with a certain recursive internal structure. This arises from the special properties of an automata-theoretic algorithm which can be used to solve the inverse problem for phase-type distributions: the construction of a Markov chain with specified absorption time distribution.

KW - Markov chains

KW - Phase-type distributions

KW - first passage times

KW - generating functions

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Phase-type distributions and the structure of finite Markov chains

Abstract

Keywords

ASJC Scopus subject areas

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