@book{54bd88650aa148a3847cfd123d0e6425,
title = "An orthogonal-polynomial approach to first-hitting times of birth-death processes",
abstract = "In a recent paper [J. Theor. Probab. 25 (2012) 950-980] Gong, Mao and Zhang, using the theory of Dirichlet forms, extended Karlin and McGregor's classical results on first-hitting times of a birth-death process on the nonnegative integers by establishing a representation for the Laplace transform $\mathbb{E}[e^{sT_{ij}}]$ of the first-hitting time $T_{ij}$ for {\em any} pair of states $i$ and $j$, as well as asymptotics for $\mathbb{E}[e^{sT_{ij}}]$ when either $i$ or $j$ tends to infinity. It will be shown here that these results may also be obtained by employing tools from the orthogonal-polynomial toolbox used by Karlin and McGregor, in particular {\em associated polynomials} and {\em Markov's Theorem}.",
keywords = "First-hitting time, Orthogonal polynomials, Associated polynomials, Markov's Theorem, MSC-42C05, MSC-60J80, Birth-death process",
author = "{van Doorn}, {Erik A.}",
note = "The second file is the latest (online first, open access) version.",
year = "2015",
month = apr,
language = "English",
series = "Memorandum of the Department of Applied Mathematics",
publisher = "University of Twente",
number = "2044",
address = "Netherlands",
}