Electronic Journal of Probability

Exponential ergodicity for general continuous-state nonlinear branching processes

Abstract

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

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

Dates
Accepted: 3 October 2020
First available in Project Euclid: 12 October 2020

https://projecteuclid.org/euclid.ejp/1602489723

Digital Object Identifier
doi:10.1214/20-EJP528

Citation

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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