 The joint distribution of sojourn times in finite semi-Markov processesAttila Csenki Stochastic Processes and their Applications, 1991, vol. 39, issue 2, 287-299 Abstract: Let Y={Yt:t[greater-or-equal, slanted]0} be a semi-Markov process whose state space S is finite. Assume that Y is either irreducible and S is then partitioned into two classes A1, A2, or that Y is absorbing and S is partitioned into A1, A2, A3, where A3 is the set of all absorbing states of Y. Denoting by TAi,j the jth sojourn of Y in Ai, i=1, 2, we determine the Laplace transform of the joint distribution of T={TAi,j:i=1, 2; J=1,..., m}. This result is derived from a recurrence relation for the Laplace transform of T. The proof of the recurrence relation itself is based on what could be called a 'generalized renewal argument'. Some known results on sojourn times in Markov and semi-Markov processes are also rederived using our main theorem. A procedure for obtaining the Laplace transform of the vector of sojourn times in special cases if S is partitioned into more than two non-absorbing classes is also considered. Keywords: sojourn; time; semi-Markov; process; Markov; process; Laplace; transform; renewal; theory; reliability; modelling (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:39:y:1991:i:2:p:287-299 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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