Representations for the decay parameter of a birth-death process based on the Courant-Fischer theorem

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Abstract

We study the decay parameter (the rate of convergence of the transition probabilities) of a birth-death process on $\{0,1,...\}$, which we allow to evanesce by escape, via state 0, to an absorbing state -1. Our main results are representations for the decay parameter under four different scenarios, derived from a unified perspective involving Karlin and McGregor’s representation for the transition probabilities of a birth-death process, and the Courant-Fischer theorem on eigenvalues of a symmetric matrix. We also show how the representations readily yield some upper and lower bounds that have appeared in the literature.
Original languageUndefined
Pages (from-to)278-289
Number of pages12
JournalJournal of applied probability
Volume52
Issue number1
DOIs
Publication statusPublished - 2015

Keywords

  • EWI-25938
  • MSC-60J80
  • MSC-42C05
  • Rate of convergence
  • IR-95642
  • Birth-death process
  • Exponential decay
  • METIS-312552
  • Orthogonal polynomials

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