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Markov renewal processes, counters and repeated sequences in Markov chains

Published online by Cambridge University Press:  01 July 2016

J. D. Biggins and
C. Cannings
J. D. Biggins*
Affiliation:
The University of Sheffield
C. Cannings*
Affiliation:
The University of Sheffield
*
∗ Postal address: Department of Probability and Statistics, The University of Sheffield, Sheffield S10 2TN, UK.
∗ Postal address: Department of Probability and Statistics, The University of Sheffield, Sheffield S10 2TN, UK.
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Abstract

The theory of Markov renewal processes is applied to study the occurrence of specific sequences of states in a Markov chain. Çinlar&s (1969) results are used to study both the basic process, and that obtained when the overlap of sequences is not permitted, as in the theory of counters. These results are applied to the fragments formed when DNA is digested using one, or more, restriction enzymes.

Keywords

SEMI-MARKOVDNA SEQUENCESENDONUCLEASESSEQUENCE PATTERNS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 3 , September 1987, pp. 521 - 545
Copyright
Copyright © Applied Probability Trust 1987 

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