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

被引：0

作者：

Ma, Rugang ^{[1
,2
]}

Zhou, Xiaowen ^{[2
]}

机构：

[1] Cent Univ Finance & Econ, Sch Stat & Math, Beijing, Peoples R China

[2] Concordia Univ, Dept Math & Stat, Montreal, PQ, Canada

来源：

JOURNAL OF APPLIED PROBABILITY | 2024年 / 61卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Continuous-state branching processes; competition; random environment; explosion; CONTINUOUS-TIME; EXTINCTION;

D O I：

10.1017/jpr.2023.32

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We find sufficient conditions on explosion/non-explosion for continuous-state branching processes with competition in a Levy 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 Levy measure of the associated branching mechanism is stable.

引用

页码：68 / 81

页数：14

共 27 条

[1] Branching processes with interaction and a generalized Ray-Knight Theorem [J].

Ba, Mamadou ;

Pardoux, Etienne .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2015, 51 (04) :1290-1313

[2] Extinction rate of continuous state branching processes in critical Levy environments [J].

Bansaye, Vincent ;

Carlos Pardo, Juan ;

Smadi, Charline .

ESAIM-PROBABILITY AND STATISTICS, 2021, 25 :346-375

[3] Scaling limits of population and evolution processes in random environment [J].

Bansaye, Vincent ;

Caballero, Maria-Emilia ;

Meleard, Sylvie .

ELECTRONIC JOURNAL OF PROBABILITY, 2019, 24

[4] On the extinction of continuous state branching processes with catastrophes [J].

Bansaye, Vincent ;

Pardo Millan, Juan Carlos ;

Smadi, Charline .

ELECTRONIC JOURNAL OF PROBABILITY, 2013, 18 :1-31

[5] Ray-Knight representation of flows of branching processes with competition by pruning of Levy trees [J].

Berestycki, J. ;

Fittipaldi, M. C. ;

Fontbona, J. .

PROBABILITY THEORY AND RELATED FIELDS, 2018, 172 (3-4) :725-788

[6]

Böinghoff C, 2012, MARKOV PROCESS RELAT, V18, P269

[7]

Chen M., 1986, ACTA MATH SINICA, V2, P121

[8]

Chen M.F., 1986, JUMP PROCESSES INTER

[9]

Chen M.-F., 2004, From Markov Chains to Non-Equilibrium Particle Systems, V2nd

[10] Continuous-state branching processes with competition: duality and reflection at infinity [J].

Foucart, Clement .

ELECTRONIC JOURNAL OF PROBABILITY, 2019, 24

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