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Birth-death processes with killing

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  • van Doorn, Erik A.
  • Zeifman, Alexander I.
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    Abstract

    The purpose of this note is to point out that Karlin and McGregor's integral representation for the transition probabilities of a birth-death process on a semi-infinite lattice with an absorbing bottom state remains valid if one allows the possibility of absorption into the bottom state from any other state. Conditions for uniqueness of the minimal transition function are also given.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-4F9N5RY-1/2/e0b7102c0ef2bda692a955b59fde6bc7
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 72 (2005)
    Issue (Month): 1 (April)
    Pages: 33-42

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    Handle: RePEc:eee:stapro:v:72:y:2005:i:1:p:33-42

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    Related research

    Keywords: Karlin-McGregor representation Orthogonal polynomials Transition function Transition probabilities State-dependent killing rate Total catastrophe;

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    Cited by:
    1. van Doorn, Erik A., 2012. "Conditions for the existence of quasi-stationary distributions for birth–death processes with killing," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2400-2410.

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