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The convergence of Cesaro averages for certain nonstationary Markov chains

Author

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  • Bowerman, Bruce
  • David, H. T.
  • Isaacson, Dean

Abstract

If P is a stochastic matrix corresponding to a stationary, irreducible, positive persistent Markov chain of period d>1, the powers Pn will not converge as n --> [infinity]. However, the subsequences Pnd+k for k=0,1,...d-1, and hence Cesaro averages [Sigma]nk-1 Pk/n, will converge. In this paper we determine classes of nonstationary Markov chains for which the analogous subsequences and/or Cesaro averages converge and consider the rates of convergence. The results obtained are then applied to the analysis of expected average cost.

Suggested Citation

  • Bowerman, Bruce & David, H. T. & Isaacson, Dean, 1977. "The convergence of Cesaro averages for certain nonstationary Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 5(3), pages 221-230, July.
    • Handle: RePEc:eee:spapps:v:5:y:1977:i:3:p:221-230
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    Cited by:

    1. Gerontidis, Ioannis I., 1995. "Periodicity of the profile process in Markov manpower systems," European Journal of Operational Research, Elsevier, vol. 85(3), pages 650-669, September.
    2. Manuel L. Esquível & Nadezhda P. Krasii & Gracinda R. Guerreiro, 2021. "Open Markov Type Population Models: From Discrete to Continuous Time," Mathematics, MDPI, vol. 9(13), pages 1-29, June.

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