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Extinction of branching symmetric α-stable processes

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Yuichi Shiozawa
Yuichi Shiozawa*
Affiliation:
Tohoku University
*
∗Postal address: Mathematical Institute, Tohoku University, Aoba, Sendai, 980-8578, Japan. Email address: [email protected]
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Abstract

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We give a criterion for extinction or local extinction of branching symmetric α-stable processes in terms of the principal eigenvalue for time-changed processes of symmetric α-stable processes. Here the branching rate and the branching mechanism are spatially dependent. In particular, the branching rate is allowed to be singular with respect to the Lebesgue measure. We apply this criterion to some branching processes.

Keywords

Branching processextinctionlocal extinctionBrownian motionsymmetric α-stable processtime changeprincipal eigenvaluegaugeability

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G52: Stable processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 4 , December 2006 , pp. 1077 - 1090
Copyright
© Applied Probability Trust 2006 

Footnotes

Dedicated to Professor Masatoshi Fukushima on the occasion of his seventieth birthday.

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