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General solidarity theorems for semi-Markov processes
- Source :
- Journal of Applied Probability. 9:789-802
- Publication Year :
- 1972
- Publisher :
- Cambridge University Press (CUP), 1972.
-
Abstract
- Let {Zt, t ≧ 0} be an irreducible regular semi-Markov process with transition probabilities Pij (t). Let f(t) be non-negative and non-decreasing to infinity, and let λ ≧ 0. This paper identifies a large set of functions f(t) with the solidarity property that convergence of the integral ≧ eλtf(t)Pij (t) dt for a specific pair of states i and j implies convergence of the integral for all pairs of states. Similar results are derived for the Markov renewal functions Mij (t). Among others it is shown that f(t) can be taken regularly varying.
- Subjects :
- Statistics and Probability
Markov chain
media_common.quotation_subject
General Mathematics
Markov process
Infinity
Slowly varying function
Combinatorics
symbols.namesake
Large set (Ramsey theory)
Markov renewal process
Convergence (routing)
symbols
Statistics, Probability and Uncertainty
media_common
Mathematics
Subjects
Details
- ISSN :
- 14756072 and 00219002
- Volume :
- 9
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Probability
- Accession number :
- edsair.doi.dedup.....c7567f1e06c281ef06938467bfbdb5eb