Renewal sequences with periodic dynamics

  • Authors:

  • Brian Fralix;James Livsey;Robert Lund

  • Affiliations:

  • Department of mathematical sciences, clemson university, clemson, sc 29634-0975. e-mail: bfralix@clemson.edu/ jlivsey@clemson.edu/ lund@clemson.edu;Department of mathematical sciences, clemson university, clemson, sc 29634-0975. e-mail: bfralix@clemson.edu/ jlivsey@clemson.edu/ lund@clemson.edu;Department of mathematical sciences, clemson university, clemson, sc 29634-0975. e-mail: bfralix@clemson.edu/ jlivsey@clemson.edu/ lund@clemson.edu

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

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.