Exponential ergodicity for general continuous-state nonlinear branching processes

TL;DR

This paper establishes conditions under which general continuous-state nonlinear branching processes exhibit exponential ergodicity, even with minimal noise, using coupling techniques and focusing on Wasserstein and total variation metrics.

Contribution

It provides new sufficient conditions for exponential and strong ergodicity of nonlinear branching processes with dissipative drifts and minimal noise, expanding understanding of their long-term behavior.

Findings

Exponential ergodicity in Wasserstein and total variation norms.

Conditions allowing vanishing diffusion or jump noise.

Criteria for strong ergodicity.

Abstract

By using the coupling technique, 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.