Birth-death Processes with Killing
نویسندگان
چکیده
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.
منابع مشابه
Birth-death Processes with Killing: Orthogonal Polynomials and Quasi-stationary Distributions
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 (killing) is possible from any state rather than just one state. The purpose of this paper is to in...
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تاریخ انتشار 2004