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Asymptotic Behavior of Continuous-Time Markov Chains

  1. Eylem Tekin

Published Online: 14 JAN 2011

DOI: 10.1002/9780470400531.eorms0063

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Tekin, E. 2011. Asymptotic Behavior of Continuous-Time Markov Chains. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. Texas A&M University, Department of Industrial and Systems Engineering, College Station, Texas

Publication History

  1. Published Online: 14 JAN 2011

Abstract

This article summarizes the theoretical foundations for analyzing the asymptotic behavior of continuous-time Markov chains. We first introduce several concepts for classifying the states of a continuous-time Markov chain. These concepts include irreducibility, recurrence, and transience. Then, we describe how to compute the limiting distribution of a continuous-time Markov chain.

Keywords:

  • continuous-time Markov chains;
  • discrete-time Markov chains;
  • asymptotic behavior;
  • balance equation;
  • reducible Markov chains;
  • irreducible Markov chains