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A Sufficient Condition for Continuous-Time Finite Skip-Free Markov Chains to Have Real Eigenvalues

In: Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Author

Listed:
  • Michael C. H. Choi

    (Cornell University, School of Operations Research and Information Engineering)

  • Pierre Patie

    (Cornell University, School of Operations Research and Information Engineering)

Abstract

We provide a sufficient condition for the negative of the infinitesimal generator of a continuous-time finite skip-free Markov chain to have only real and non-negative eigenvalues. The condition includes stochastic monotonicity and certain requirements on the transition rates of the chain. We also give a sample path illustration of Markov chains that satisfy the conditions and its Siegmund dual. We illustrate our result by detailing an example which also reveals that our conditions are not necessary.

Suggested Citation

  • Michael C. H. Choi & Pierre Patie, 2016. "A Sufficient Condition for Continuous-Time Finite Skip-Free Markov Chains to Have Real Eigenvalues," Springer Books, in: Jacques Bélair & Ian A. Frigaard & Herb Kunze & Roman Makarov & Roderick Melnik & Raymond J. Spiteri (ed.), Mathematical and Computational Approaches in Advancing Modern Science and Engineering, pages 529-536, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30379-6_48
    DOI: 10.1007/978-3-319-30379-6_48
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