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Limit Theorems for Renewal Processes

  1. Nan Liu

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0468

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Liu, N. 2011. Limit Theorems for Renewal Processes. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. Mailman School of Public Health, Columbia University, Department of Health Policy and Management, New York, New York

Publication History

  1. Published Online: 15 FEB 2011

Abstract

This article describes the key renewal theorem and the Blackwell's renewal theorem. These two limit theorems for renewal processes are equivalent but of different forms. They are particularly useful for characterizing the asymptotic behavior of a probabilistic quantity of interest in a renewal process. We present two classical applications of these limit theorems: the limiting distributions of recurrence times in a renewal process and the asymptotic expansion of a renewal function. Further readings on the theoretical development of these limit theorems and their applications in different areas are also provided.

Keywords:

  • renewal process;
  • key renewal theorem;
  • Blackwell's renewal theorem;
  • current age;
  • remaining life (excess life);
  • total life;
  • inspection paradox