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

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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.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, The University of New Mexico, Albuquerque, NM, 87131, USA

    José Luis Palacios

  2. Department of Mathematics, London School of Economics, London, WC2A 2AE, UK

    Daniel Quiroz

Authors
  1. José Luis Palacios
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  2. Daniel Quiroz
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Correspondence to José Luis Palacios.

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Palacios, J.L., Quiroz, D. Birth and Death Chains on Finite Trees: Computing their Stationary Distribution and Hitting Times. Methodol Comput Appl Probab 18, 487–498 (2016). https://doi.org/10.1007/s11009-014-9436-1

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  • DOI: https://doi.org/10.1007/s11009-014-9436-1

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