Birth-death processes with killing

Erik A. van Doorn, Alexander I. Zeifman

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    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.
    Original languageEnglish
    Pages (from-to)33-42
    Number of pages10
    JournalStatistics & probability letters
    Issue number1
    Publication statusPublished - 2005


    • Karlin–McGregor representation
    • Orthogonal polynomials
    • Transition function
    • Transition probabilities
    • State-dependent killing rate
    • Total catastrophe


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    • Birth-death processes with killing

      van Doorn, E. A. & Zeifman, A. I., 2004, Enschede: University of Twente. 12 p. (Memorandum Faculty of Mathematical Sciences; no. 1715)

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