Electronic Journal of Probability

Exponential ergodicity for general continuous-state nonlinear branching processes

Pei-Sen Li and Jian Wang

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By combining the coupling by reflection for Brownian motion with the refined basic coupling for Poisson random measure, we present sufficient conditions for the exponential ergodicity of general continuous-state nonlinear branching processes in both the $L^{1}$-Wasserstein distance and the total variation norm, where the drift term is dissipative only for large distance, and either diffusion noise or jump noise is allowed to be vanished. Sufficient conditions for the corresponding strong ergodicity are also established.

Article information

Electron. J. Probab., Volume 25 (2020), paper no. 125, 25 pp.

Received: 13 September 2019
Accepted: 3 October 2020
First available in Project Euclid: 12 October 2020

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Primary: 60G51: Processes with independent increments; Lévy processes 60G52: Stable processes 60J25: Continuous-time Markov processes on general state spaces 60J75: Jump processes

continuous-state nonlinear branching process exponential ergodicity coupling strong ergodicity

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Li, Pei-Sen; Wang, Jian. Exponential ergodicity for general continuous-state nonlinear branching processes. Electron. J. Probab. 25 (2020), paper no. 125, 25 pp. doi:10.1214/20-EJP528. https://projecteuclid.org/euclid.ejp/1602489723

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