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Birth and Death Chains on Finite Trees: Computing their Stationary Distribution and Hitting Times

Author

Listed:
  • José Luis Palacios

    (The University of New Mexico)

  • Daniel Quiroz

    (Department of Mathematics, London School of Economics)

Abstract

Every birth and death chain on a finite tree can be represented as a random walk on the underlying tree endowed with appropriate conductances. We provide an algorithm that finds these conductances in linear time. Then, using the electric network approach, we find the values for the stationary distribution and for the expected hitting times between any two vertices in the tree. We show that our algorithms improve classical procedures: they do not exhibit ill-posedness and the orders of their complexities are smaller than those of traditional algorithms found in the literature.

Suggested Citation

  • José Luis Palacios & Daniel Quiroz, 2016. "Birth and Death Chains on Finite Trees: Computing their Stationary Distribution and Hitting Times," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 487-498, June.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:2:d:10.1007_s11009-014-9436-1
    DOI: 10.1007/s11009-014-9436-1
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    References listed on IDEAS

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    1. Adolfo Quiroz, 1989. "Fast random generation of binary, t-ary and other types of trees," Journal of Classification, Springer;The Classification Society, vol. 6(1), pages 223-231, December.
    2. Palacios, JoséLuis & Tetali, Prasad, 1996. "A note on expected hitting times for birth and death chains," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 119-125, October.
    3. Palacios, José Luis, 2009. "On hitting times of random walks on trees," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 234-236, January.
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    Cited by:

    1. Greg Markowsky & José Luis Palacios, 2019. "Symmetry in the Green’s Function for Birth-death Chains," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 841-851, September.

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