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Markov Renewal Processes

  1. Serhan Ziya

Published Online: 14 JAN 2011

DOI: 10.1002/9780470400531.eorms0498

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Ziya, S. 2011. Markov Renewal Processes. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. University of North Carolina, Department of Statistics and Operations Research, Chapel Hill, North Carolina

Publication History

  1. Published Online: 14 JAN 2011

Abstract

A Markov renewal process is a vector valued counting process that keeps track of the number of certain types of events associated with a stochastic process. It is a generalization of a renewal process in that a Markov renewal process with a single-dimensional state representation is a renewal process. In this article, we first define Markov renewal sequences, which are at the core of Markov renewal processes. Then, we give a formal description of Markov renewal processes and provide a number of examples where these processes appear.

Keywords:

  • renewal process;
  • Markov renewal sequence;
  • Markov renewal process;
  • stochastic process;
  • stochastic vector process