Ratio limits and limiting conditional distributions for discrete-time birth-death processes

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Doorn van, Erik A. and Schrijner, Pauline (1995) Ratio limits and limiting conditional distributions for discrete-time birth-death processes. Journal of Mathematical Analysis and Applications, 190 (1). pp. 263-284. ISSN 0022-247X

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Abstract:We consider discrete-time birth-death processes with an absorbing state and study the conditional state distribution at time n given that absorption has not occurred by that time but will occur eventually. In particular, we establish conditions for the convergence of these distributions to a proper distribution as n→∞. The problem turns out to be closely related to that of finding conditions for the existence of limits of ratios of n-step transition probabilities as n→∞. Orthogonal polynomials feature in the spectral representation for the n-step transition probabilities of a birth-death process and, consequently, play a key role in the analysis.
Item Type:Article
Copyright:© 1995 Elsevier Science
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/30100
Official URL:http://dx.doi.org/10.1006/jmaa.1995.1076
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