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DECOMPOSITION OF A SEMI‐MARKOV PROCESS UNDER A MARKOVIAN RULE
Author(s) -
Cinlar E.
Publication year - 1966
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1966.tb00266.x
Subject(s) - markov chain , markov process , combinatorics , mathematics , decomposition , event (particle physics) , process (computing) , discrete mathematics , computer science , physics , statistics , chemistry , quantum mechanics , organic chemistry , operating system
Summary Consider a semi‐Markov process {X(t), t>0} with transition epochs T 0 T 1 , T 2 …. Suppose that at each one of the epochs {T n } one of R possible events, E 1 , E 2 ,…, E R can happen, where the occurrences of successive events form a Markov chain. for a fixed r, let the times the event E r happens be U o U 1 , U 2 ,…. In this paper we are interested in the process {Y(t), t>0)} where Y(t)=X(U k ) if and only if U k ≤t