Statistics Seminars: Birth-death processes with killing: Orthogonal polynomials and quasi-stationary distributions.
27 May 2005 00:00 in CM107
"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. In the talk I will discuss to what extent properties of birth-death processes, in particular with regard to the existence and shape of quasi-stationary distributions (initial distributions which are such that the state distribution of the process, conditional on non-absorption, is constant over time), 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 becomes more elaborate otherwise. (The talk is based on joint work with P. Coolen-Schrijner and A. Zeifman.) "
"CM221, 4.15 - 5.00 pm"
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