@book{246b76d95ab346969e1208ba2e4f9083,

title = "Extinction probability in a birth-death process with killing",

abstract = "We study birth-death processes on the non-negative integers where $\{1,2,\ldots\}$ is an irreducible class and $0$ an absorbing state, with the additional feature that a transition to state $0$ may occur from any state. We give a condition for absorption (extinction) to be certain and obtain the eventual absorption probabilities when absorption is not certain. We also study the rate of convergence as $t\to\infty$ of the probability of absorption at time $t$, and relate it to the common rate of convergence of the transition probabilities which do not involve state $0$. Finally, we derive upper and lower bounds for the probability of absorption at time $t$ by applying a technique which involves the logarithmic norm of an appropriately defined operator.",

keywords = "MSC-60J27, MSC-60J80, IR-65907, METIS-218214, EWI-3543",

author = "{van Doorn}, {Erik A.} and A.I. Zeifman",

note = "Imported from MEMORANDA",

year = "2004",

language = "Undefined",

series = "Memorandum Faculty of Mathematical Sciences",

publisher = "University of Twente, Faculty of Mathematical Sciences",

number = "1723",

}