@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 = "IR-95675, METIS-312553, First-hitting time, EWI-25939, 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 = "Undefined",

series = "Memorandum of the Department of Applied Mathematics",

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

number = "2044",

}