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Monotone matrices and monotone Markov processes


  • Keilson, Julian
  • Kester, Adri


A stochastic matrix is "monotone" [4] if its row-vectors are stochastically increasing. Closure properties, characterizations and the availability of a second maximal eigenvalue are developed. Such monotonicity is present in a variety of processes in discrete and continous time. In particular, birth-death processes are monotone. Conditions for the sequential monotonicity of a process are given and related inequalities presented.

Suggested Citation

  • Keilson, Julian & Kester, Adri, 1977. "Monotone matrices and monotone Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 5(3), pages 231-241, July.
  • Handle: RePEc:eee:spapps:v:5:y:1977:i:3:p:231-241

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    11. Nico M. van Dijk & Masakiyo Miyazawa, 2004. "Error Bounds for Perturbing Nonexponential Queues," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 525-558, August.
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    13. Kuber, Madhuri & Dharmadhikari, Avinash, 1996. "Association in time of a finite semi-Markov process," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 125-133, February.
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    18. Pekergin, Nihal & Dayar, Tugrul & Alparslan, Denizhan N., 2005. "Componentwise bounds for nearly completely decomposable Markov chains using stochastic comparison and reordering," European Journal of Operational Research, Elsevier, vol. 165(3), pages 810-825, September.


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