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On the relation between reversibility and monotonicity of fluctuation spectra for discrete time finite state Markov chains


  • Chen, Yong
  • Qian, Min-Ping
  • Xie, Jian-Sheng


For the irreducible aperiodic discrete time finite state Markov chain, (i) if it is reversible, we provide a necessary and sufficient condition for all fluctuation spectra to be monotonic on and (ii) if it is irreversible, then there exist some nonmonotonic fluctuation spectra.

Suggested Citation

  • Chen, Yong & Qian, Min-Ping & Xie, Jian-Sheng, 2008. "On the relation between reversibility and monotonicity of fluctuation spectra for discrete time finite state Markov chains," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2258-2264, October.
  • Handle: RePEc:eee:stapro:v:78:y:2008:i:14:p:2258-2264

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    References listed on IDEAS

    1. Kyriakidis, E. G., 1994. "Stationary probabilities for a simple immigration-birth-death process under the influence of total catastrophes," Statistics & Probability Letters, Elsevier, vol. 20(3), pages 239-240, June.
    2. Economou, Antonis & Fakinos, Demetrios, 2003. "A continuous-time Markov chain under the influence of a regulating point process and applications in stochastic models with catastrophes," European Journal of Operational Research, Elsevier, vol. 149(3), pages 625-640, September.
    3. Peng, NanFu & Pearl, Dennis K. & Chan, Wenyaw & Bartoszynski, Robert, 1993. "Linear birth and death processes under the influence of disasters with time-dependent killing probabilities," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 243-258, April.
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