论文标题
分支机构随着移民和竞争的指数型成分
Exponential ergodicity of branching processes with immigration and competition
论文作者
论文摘要
我们研究了随着移民和竞争的连续国家分支过程的千古特性。在自然假设下证明了加权总变化距离中的指数型成分。主要定理适用于亚临界，关键和超临界的分支机制，包括所有稳定类型的分支机制。该证明是基于马尔可夫耦合过程的构建以及距离的非对称控制函数的选择。这些旨在从州空间的不同地区的分支，移民和竞争机制中识别和利用主导因素的优势。该方法提供了一种找到恐怖率的下限的方法。
We study the ergodic property of a continuous-state branching process with immigration and competition. The exponential ergodicity in a weighted total variation distance is proved under natural assumptions. The main theorem applies to subcritical, critical and supercritical branching mechanisms, including all those of stable types. The proof is based on the construction of a Markov coupling process and the choice of a nonsymmetric control function for the distance. Those are designed to identify and to take the advantage of the dominating factor from the branching, immigration and competition mechanisms in different parts of the state space. The approach provides a way of finding a lower bound of the ergodicity rate.
