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Explosion of continuous-state branching processes with competition in a Lévy environment

Part of: Markov processes Stochastic analysis

Published online by Cambridge University Press:  09 June 2023

Rugang Ma  and
Xiaowen Zhou
Rugang Ma*
Affiliation:
Central University of Finance and Economics
Xiaowen Zhou*
Affiliation:
Concordia University
*
*Postal address: School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China; Department of Mathematics and Statistics, Concordia University, Montreal, Canada. Email address: marg@cufe.edu.cn
**Postal address: Department of Mathematics and Statistics, Concordia University, Montreal, Canada. Email address: xiaowen.zhou@concordia.ca
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Abstract

We find sufficient conditions on explosion/non-explosion for continuous-state branching processes with competition in a Lévy random environment. In particular, we identify the necessary and sufficient conditions on explosion/non-explosion when the competition function is a power function and the Lévy measure of the associated branching mechanism is stable.

Keywords

Continuous-state branching processescompetitionrandom environmentexplosion

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60H20: Stochastic integral equations
Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 1 , March 2024 , pp. 68 - 81
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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