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Technical Note—An Eigenvector Condition for Markov Chain Lumpability

Author

Listed:
  • D. R. Barr

    (Naval Postgraduate School, Monterey, California)

  • M. U. Thomas

    (Naval Postgraduate School, Monterey, California)

Abstract

Under certain conditions the state space of a discrete parameter Markov chain may be partitioned to form a smaller “lumped” chain that retains the Markov property. Existing statements of conditions on the transition matrix P of the original chain characterizing such lumpability are difficult to verify in practice, especially when the dimension of P is large. An alternate approach, based on the eigenvectors of P , is presented and illustrated with examples.

Suggested Citation

  • D. R. Barr & M. U. Thomas, 1977. "Technical Note—An Eigenvector Condition for Markov Chain Lumpability," Operations Research, INFORMS, vol. 25(6), pages 1028-1031, December.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:6:p:1028-1031
    DOI: 10.1287/opre.25.6.1028
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    Cited by:

    1. Georgiou, K. & Domazakis, G.N. & Pappas, D. & Yannacopoulos, A.N., 2021. "Markov chain lumpability and applications to credit risk modelling in compliance with the International Financial Reporting Standard 9 framework," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1146-1164.
    2. Roy Cerqueti & Paolo Falbo & Cristian Pelizzari & Federica Ricca & Andrea Scozzari, 2017. "A mixed integer linear program to compress transition probability matrices in Markov chain bootstrapping," Annals of Operations Research, Springer, vol. 248(1), pages 163-187, January.

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