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RENEWAL SEQUENCES WITH PERIODIC DYNAMICS

Published online by Cambridge University Press:  25 November 2011

Brian Fralix ,
James Livsey  and
Robert Lund
Brian Fralix
Affiliation:
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975. E-mail: bfralix@clemson.edu; jlivsey@clemson.edu; lund@clemson.edu
James Livsey
Affiliation:
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975. E-mail: bfralix@clemson.edu; jlivsey@clemson.edu; lund@clemson.edu
Robert Lund
Affiliation:
Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975. E-mail: bfralix@clemson.edu; jlivsey@clemson.edu; lund@clemson.edu
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Abstract

Discrete-time renewal sequences play a fundamental role in the theory of stochastic processes. This article considers periodic versions of such processes; specifically, the length of an interrenewal is allowed to probabilistically depend on the season at which it began. Using only elementary renewal and Markov chain techniques, computational and limiting aspects of periodic renewal sequences are investigated. We use these results to construct a time series model for a periodically stationary sequence of integer counts.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 1 , January 2012 , pp. 1 - 15
Copyright
Copyright © Cambridge University Press 2011

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