Random walks with similar transition probabilities

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4 Citations (Scopus)

Abstract

We consider random walks on the nonnegative integers with a possible absorbing state at -1. A random walk ? is called α-similar to a random walk ? if there exist constants Cij such that for the corresponding n-step transition probabilities P̃ ij (n)=α-nCijPij (n), i,j≥0, hold. We give necessary and sufficient conditions for the α-similarity of two random walks both in terms of the parameters and in terms of the corresponding spectral measures which appear in the spectral representation of the n-step transition probabilities developed by Karlin and McGregor.

Original languageEnglish
Pages (from-to)423-432
Number of pages10
JournalJournal of Computational and Applied Mathematics
Volume153
Issue number1-2
DOIs
Publication statusPublished - 1 Apr 2003
Externally publishedYes

Keywords

  • Random walk measures
  • Random walk polynomials
  • Similar random walks
  • Transition probabilities

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