Exponential ergodicity of CBIRE-processes with competition and catastrophes

Shukai Chen, Rongjuan Fang, Lina Ji and Jian Wang

Stochastic Processes and their Applications, 2026, vol. 192, issue C

Abstract: We establish the exponential ergodicity in a weighted total variation distance of continuous-state branching processes with immigration in random environments with competition and catastrophes, under a Lyapunov-type condition and other mild assumptions. The proof is based on a Markov coupling process along with some delicate estimates for the associated coupling generator. In particular, the main result indicates whether and how the competition mechanism, the random environment and the catastrophe could balance the branching mechanism respectively to guarantee the exponential ergodicity of the processes.

Keywords: Branching process; Random environment; Competition; Catastrophe; Exponential ergodicity; Markov coupling (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.spa.2025.104807

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