唯一拟平稳分布，以及可能稳定的灭绝
Unique Quasi-Stationary Distribution, with a possibly stabilizing extinction
AI总结：
本文建立了全变差范数下指数收敛到唯一拟平稳分布及Q-过程指数遍历性的充分条件，通过基于Harris递归的耦合程序适用于一般连续时间和连续空间Markov过程，并引入依赖最终时间范围和初始分布的耦合步骤，最后以生灭过程和扩散过程为例进行说明。
摘要：
我们建立了在全变差范数下指数收敛到唯一拟平稳分布的充分条件。这些条件也确保了Q-过程（即条件为永远不被吸收的过程）的存在性与指数遍历性。该技术依赖于与Harris递归（针对Markov链）相关的耦合程序。它适用于一般的连续时间和连续空间Markov过程。主要的新颖之处在于，我们根据生存的最终时间范围和初始分布来调节每个耦合步骤。通过这种方式，我们能够显著地将初始条件的依赖性纳入收敛中。作为示例，我们考虑了带有灾难的连续时间生灭过程，以及描述（局部）种群适应其环境的扩散过程。
英文摘要：
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process conditionned upon never being absorbed. The technique relies on a coupling procedure that is related to Harris recurrence (for Markov Chains). It applies to general continuous-time and continuous-space Markov processes. The main novelty is that we modulate each coupling step depending both on a final horizon of time (for survival) and on the initial distribution. By this way, we could notably include in the convergence a dependency on the initial condition. As an illustration, we consider a continuous-time birth-death process with catastrophes and a diffusion process describing a (localized) population adapting to its environment.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
