Markov renewal processes, counters and repeated sequences in Markov chains

Authors
Biggins, J.D. Cannings, C.
Citation
Biggins, J.d et C. Cannings,, Markov renewal processes, counters and repeated sequences in Markov chains, Advances in applied probability , 19(3), 1987, pp. 521-545
Journal title
Advances in applied probability → ACNP
ISSN journal
00018678
Volume
19
Issue
3
Year of publication
1987
Pages
521 - 545
Database
ACNP
SICI code
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.