带竞争与灾变的CBIRE过程的指数遍历性
Exponential Ergodicity of CBIRE-Processes with Competition and Catastrophes
AI总结：
本文在Lyapunov型条件下，通过马尔可夫耦合与耦合生成元精细估计，证明带竞争与灾变的CBIRE过程的指数遍历性，明确三类因素平衡分支机制以保障遍历性的作用。
摘要：
我们在Lyapunov型条件及其他温和假设下，建立了带竞争与灾变的随机环境中带移民连续状态分支过程（CBIRE过程）在加权全变差距离下的指数遍历性。证明基于马尔可夫耦合过程及对相关耦合生成元的精细估计。特别地，主要结果揭示了竞争机制、环境与灾变分别能否及如何平衡分支机制，以保证过程的指数遍历性。
英文摘要：
We establish the exponential ergodic property 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 environment and the catastrophe could balance the branching mechanism respectively to guarantee the exponential ergodicity of the process.
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