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Extinction and coming down from infinity of continuous-state branching processes with competition in a Lévy environment

Part of: Markov processes

Published online by Cambridge University Press:  25 February 2021

H. Leman  and
J. C. Pardo
H. Leman*
Affiliation:
Université de Lyon, Inria, CNRS, ENS de Lyon, UMPA
J. C. Pardo*
Affiliation:
Centro de Investigación en Matemáticas A.C.
*
*Postal address: Université de Lyon, Inria, CNRS, ENS de Lyon, UMPA UMR 5669, 46 allée d’Italie, 69364 Lyon, France.
**Postal address: Centro de Investigación en Matemáticas A.C. Calle Jalisco s/n. 36240 Guanajuato, México. Email address: [email protected]
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Abstract

We are interested in the property of coming down from infinity of continuous-state branching processes with competition in a Lévy environment. We first study the event of extinction for such a family of processes under Grey’s condition. Moreover, if we add an integrability condition on the competition mechanism then the process comes down from infinity regardless of the long-time behaviour of the environment.

Keywords

Continuous-state branching processes in random environmentcompetitionextinctioncoming down from infinity

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J75: Jump processes
Secondary: 60J85: Applications of branching processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 58 , Issue 1 , March 2021 , pp. 128 - 139
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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