@book{0651727c30f04530a8c673b5ced97c86,

title = "Representations for the decay parameter of a birth-death process based on the Courant-Fischer Theorem",

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 Karlin and McGregor{\textquoteright}s representation for the transition probabilities of a birth-death process, and the Courant-Fischer Theorem for eigenvalues of a symmetric matrix. We also show how the representations readily yield some upper and lower bounds that have appeared in the literature.",

keywords = "METIS-303990, Exponential decay, IR-88727, Birth-death process, Rate of convergence, Orthogonal polynomials, EWI-24292",

author = "{van Doorn}, {Erik A.}",

year = "2014",

month = jan,

language = "Undefined",

series = "Memorandum",

publisher = "University of Twente, Department of Applied Mathematics",

number = "2033",

}