Probability in the Engineering and Informational Sciences

Table of Contents - January 2012 - Volume 26, Issue 01  

Research Article

RENEWAL SEQUENCES WITH PERIODIC DYNAMICS

Brian Fralixa1, James Livseya1 and Robert Lunda1

a1 Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975. E-mail: bfralix@clemson.edu; jlivsey@clemson.edu; lund@clemson.edu

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.