Quasi-stationary distribution for continuous-state branching processes with competition

Pei Sen Li, Jian Wang, Xiaowen Zhou*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study quasi-stationary distribution of the continuous-state branching process with competition introduced by Berestycki et al. (2018). This process is defined as the unique strong solution to a stochastic integral equation with jumps. An important example is the logistic branching process proposed by Lambert (2005). We establish the strong Feller property, trajectory Feller property, Lyapunov condition, weak Feller property and irreducibility, respectively. These properties together allow us to prove that if the competition is strong enough near +∞, then there is a unique quasi-stationary distribution, which attracts all initial distributions with exponential rates.

Original languageEnglish
Article number104457
JournalStochastic Processes and their Applications
Volume177
DOIs
Publication statusPublished - Nov 2024

Keywords

  • Competition
  • Continuous-state branching process
  • Irreducibility
  • Quasi-stationary distribution
  • Strong feller property

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