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RENEWAL COUNTING PROCESS INDUCED BY A DISCRETE MARKOV CHAIN
Author(s) -
Adke S.R.,
Balakrish.
Publication year - 1992
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.1992.tb01049.x
Subject(s) - markov chain , renewal theory , markov renewal process , mathematics , set (abstract data type) , counting process , markov process , discrete mathematics , chain (unit) , key (lock) , variable order markov model , process (computing) , combinatorics , markov model , computer science , statistics , physics , computer security , astronomy , programming language , operating system
Summary Some renewal theoretic properties of a renewal counting process induced by a Markov chain on the set of non‐negative integers are established, namely, analogues of the classical elementary, Blackwell, and Breiman theorems and the key renewal theorem. These results generalize those of Vere‐Jones (1975) who considered a Markov chain on the set of positive integers.