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Birth-death processes with killing

Author

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

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.

Suggested Citation

  • van Doorn, Erik A. & Zeifman, Alexander I., 2005. "Birth-death processes with killing," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 33-42, April.
    • Handle: RePEc:eee:stapro:v:72:y:2005:i:1:p:33-42
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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.
    2. Peter Keller & Sylvie Rœlly & Angelo Valleriani, 2015. "A Quasi Random Walk to Model a Biological Transport Process," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 125-137, March.

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