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February 2018 Hitting probabilities for the Greenwood model and relations to near constancy oscillation
M. Möhle
Bernoulli 24(1): 316-332 (February 2018). DOI: 10.3150/16-BEJ878

Abstract

We derive some properties of the Greenwood epidemic Galton–Watson branching model. Formulas for the probability $h(i,j)$ that the associated Markov chain $X$ hits state $j$ when started from state $i\ge j$ are obtained. For $j\ge1$, it follows that $h(i,j)$ slightly oscillates with varying $i$ and has infinitely many accumulation points. In particular, $h(i,j)$ does not converge as $i\to\infty$. It is shown that there exists a Markov chain $Y$ which is Siegmund dual to the chain $X$. The hitting probabilities of the dual Markov chain $Y$ are investigated.

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M. Möhle. "Hitting probabilities for the Greenwood model and relations to near constancy oscillation." Bernoulli 24 (1) 316 - 332, February 2018. https://doi.org/10.3150/16-BEJ878

Information

Received: 1 November 2015; Revised: 1 March 2016; Published: February 2018
First available in Project Euclid: 27 July 2017

zbMATH: 06778330
MathSciNet: MR3706759
Digital Object Identifier: 10.3150/16-BEJ878

Keywords: branching process , Duality , Epidemic model , Greenwood model , hitting probabilities , Leader election , near constancy oscillation

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

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Vol.24 • No. 1 • February 2018
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