Birth-death processes with killing: orthogonal polynomials and quasi-stationary distributions

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Coolen-Schrijner, P. and Doorn van, E.A. (2005) Birth-death processes with killing: orthogonal polynomials and quasi-stationary distributions. [Report]

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Abstract: The Karlin-McGregor representation for the transition probabilities of a birth-death process with an absorbing bottom state involves a sequence of orthogonal polynomials and the corresponding measure. This representation can be generalized to a setting in which a transition to the absorbing state ({\em killing}) is possible from any state rather than just one state. The purpose of this paper is to investigate to what extent properties of birth-death processes, in particular with regard to the existence of quasi-stationary distributions, remain valid in the generalized setting. It turns out that the elegant structure of the theory of quasi-stationarity for birth-death processes remains intact as long as killing is possible from only finitely many states, but breaks down otherwise.
Item Type:Report
Copyright:© 2005 University of Twente, Department of Mathematics
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/65949
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Metis ID: 224146