Abstract
We study the decay parameter (the rate of convergence of the transition probabilities) of a birth-death process on {0, 1, . . .}, which we allow to evanesce by escape, via state 0, to an absorbing state -1. Our main results are representations for the decay parameter under four different scenarios, derived from a unified perspective involving the orthogonal polynomials appearing in Karlin and McGregor's representation for the transition probabilities of a birth-death process, and the Courant-Fischer theorem on eigenvalues of a symmetric matrix. We also show how the representations readily yield some upper and lower bounds that have appeared in the literature.
Citation
Erik A. van Doorn. "Representations for the decay parameter of a birth-death process based on the Courant-Fischer theorem." J. Appl. Probab. 52 (1) 278 - 289, March 2015. https://doi.org/10.1239/jap/1429282622
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