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Some Aspects of Complete Monotonicity in Time-Reversible Markov Chains

  • Mark Brown
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Part of the International Series in Operations Research & Management Science book series (ISOR, volume 19)

Abstract

It is a pleasure to participate in this birthday volume for Julian Keilson. Julian has performed distinguished research and service to the profession, and those of us who work in applied probability are deeply indebted to him. On a personal level, I have received a great deal of research inspiration from Julian’s insightful work and have greatly valued his friendship over the years.

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References

  1. [1]
    Aldous, D. J. Reversible Markov chains and random walks on graphs. Lecture notes, 1993.Google Scholar
  2. [2]
    Aldous, D. J., and Brown, M. Inequalities for rare events in time reversible Markov chains I. In: Shaked, M., and Tong, Y. L. (eds), Stochastic Inequalities, Vol. 22 of Lecture Notes. Institute of Mathematical Statistics, 1992, pp. 1–16.Google Scholar
  3. [3]
    Brown, M. Approximating IMRL distributions by exponential distributions, with applications to first passage times. Ann. Prob 11, 419–427, 1983.zbMATHCrossRefGoogle Scholar
  4. [4]
    Brown, M. Interlacing eigenvalues in time reversible Markov chains. City College, CUNY technical report, August 1994.Google Scholar
  5. [5]
    Brown, M. A useful isometry for time reversible Markov chains. City College, CUNY technical report, February 1995.Google Scholar
  6. [6]
    Diaconis, P., and Stroock, D. Geometric bounds for eigenvalues of Markov chains. Ann. Appl. Prob. 1, 36–61, 1991.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    Fill, J. A. Eigenvalue bounds on convergence to stationarity for non-reversible Markov chains with an application to the exclusion process. Ann. Appl. Prob. 1, 62–87, 1991.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    Keilson, J. Markov Chain Models, Rarity and Exponentiality. Springer-Verlag, New York, 1979.zbMATHCrossRefGoogle Scholar

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© Springer Science+Business Media New York 1999

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  • Mark Brown

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