Random walks with similar transition probabilities

We consider random walks on the nonnegative integers with a possible absorbing state at −1. A random walk X̃ is called α-similar to a random walk X if there exist constants Cij such that for the corresponding n-step transition probabilities P̃ij(n)=α−nCijPij(n), i,j⩾0, hold. We give necessary and su...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2003-04, Vol.153 (1-2), p.423-432
Main Author: Schiefermayr, Klaus
Format: Article
Language:English
Subjects:
Exact sciences and technology
Markov processes
Mathematical analysis
Mathematics
Probability and statistics
Probability theory and stochastic processes
Random walk measures
Random walk polynomials
Sciences and techniques of general use
Similar random walks
Special functions
Transition probabilities
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Summary:We consider random walks on the nonnegative integers with a possible absorbing state at −1. A random walk X̃ is called α-similar to a random walk X if there exist constants Cij such that for the corresponding n-step transition probabilities P̃ij(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.
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(02)00640-4