
SIGMA 14 (2018), 047, 9 pages arXiv:1801.00506
https://doi.org/10.3842/SIGMA.2018.047
Contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications (OPSFA14)
On the Strong Ratio Limit Property for DiscreteTime BirthDeath Processes
Erik A. van Doorn
Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Received January 03, 2018, in final form May 13, 2018; Published online May 15, 2018
Abstract
A sufficient condition is obtained for a discretetime birthdeath process to possess the strong ratio limit property, directly in terms of the onestep transition probabilities of the process. The condition encompasses all previously known sufficient conditions.
Key words:
(a)periodicity; birthdeath process; orthogonal polynomials; random walk measure; ratio limit; transition probability.
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