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A note on repeated sequences in Markov chains

Published online by Cambridge University Press:  01 July 2016

J. D. Biggins
J. D. Biggins*
Affiliation:
University of Sheffield
*
∗Postal address: Department of Probability and Statistics, The University, Sheffield S3 7RH, UK.
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Abstract

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If (non-overlapping) repeats of specified sequences of states in a Markov chain are considered, the result is a Markov renewal process. Formulae somewhat simpler than those given in Biggins and Cannings (1987) are derived which can be used to obtain the transition matrix and conditional mean sojourn times in this process.

Keywords

SEQUENCE PATTERNSMARKOV RENEWAL PROCESS
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 19 , Issue 3 , September 1987 , pp. 739 - 742
Copyright
Copyright © Applied Probability Trust 1987 

References

Biggins, J. D. (1986) On repeated sequences in Markov chains. Department of Probability and Statistics, University of Sheffield, Research Report no. 279/86.Google Scholar
Biggins, J. D. and Cannings, C. (1987) Markov renewal processes, counters and repeated sequences in Markov chains. Adv. Appl. Prob. 19, 521–545.CrossRefGoogle Scholar
Bishop, D. T., Williamson, J. A. and Skolnick, M. H. (1983) A model for restriction fragment length distributions. Am. J. Hum. Genet. 35, 795–815.Google Scholar
Gerber, H. U. and Li, S.-Y.P. (1981) The occurrence of sequence patterns in repeated experiments and hitting times in a Markov chain. Stoch. Proc. Appl. 11, 101–108.CrossRefGoogle Scholar