A localized coupling approach to interacting continuous-state branching processes
Probability
2026-04-06 v1
Abstract
We introduce a class of continuous-state branching processes with immigration, predation and competition, which can be viewed as a combination of the classical Lotka-Volterra model and continuous-state branching processes with competition that were introduced by Berestycki, Fittipaldi, and Fontbona (Probab. Theory Relat. Fields, 2018). This model can be constructed as a unique strong solution to a class of two-dimensional stochastic differential equations with jumps. We establish sharp conditions for the uniform ergodicity in the total variation of this model. Our proof relies on a novel, localized Markovian coupling approach, which is of its own interest in the ergodicity theory of Markov processes with interactions.
Keywords
Cite
@article{arxiv.2604.03030,
title = {A localized coupling approach to interacting continuous-state branching processes},
author = {Shukai Chen and Pei-Sen Li and Jian Wang},
journal= {arXiv preprint arXiv:2604.03030},
year = {2026}
}