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Persistence of a critical super-2 process

Part of: Markov processes Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

Luis G. Gorostiza ,
Kenneth J. Hochberg  and
Anton Wakolbinger
Luis G. Gorostiza*
Affiliation:
Centro de Investigación y de Estudios Avanzados, México DF
Kenneth J. Hochberg*
Affiliation:
Bar-Ilan University
Anton Wakolbinger*
Affiliation:
Johann-Wolfgang Goethe-Universität, Frankfurt am Main
*
∗Postal address: Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados, A.P. 14–740, 07300 México DF, México.
∗∗Postal address: Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel.
∗∗∗Postal address: Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, D-60054 Frankfurt am Main, Germany.
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Abstract

It is shown that the critical two-level (2, d, 1, 1)-superprocess is persistent in dimensions d greater than 4. This complements the extinction result of Wu (1994) and implies that the critical dimension is 4.

Keywords

MEASURE-VALUED PROCESSSUPERPROCESSHIERARCHICAL BRANCHINGPERSISTENCELOCAL EXTINCTION

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J60: Diffusion processes
Secondary: 60H99: None of the above, but in this section
Type
Short Communications
Information
Journal of Applied Probability , Volume 32 , Issue 2 , June 1995 , pp. 534 - 540
Copyright
Copyright © Applied Probability Trust 1995 

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