另一个定量哈里斯定理
Yet Another Quantitative Harris Theorem
摘要：
在本文中，我们建立了一个定量的哈里斯定理与有效的控制常数。我们的方法的一个好处是解耦的小集和Lyapunov-Foster漂移条件。我们的方法允许任何小集合和任何在Lyapunov-Foster条件下的集合，只要第二个满足所谓的“数量小”条件。该定理依赖于一个新的定量肯德尔型定理的证明，该定理的灵感来自一般状态空间上的马尔可夫链技术。我们给出了这种方法在混合过程的马尔可夫链逼近中的一个应用。
英文摘要：
In this paper we develop a quantitative Harris theorem with effective control over the constants. A benefit of our methodology is the decoupling of the small set and Lyapunov-Foster Drift conditions. Our methodology allows any small set and any set in the Lyapunov-Foster condition as long as the second satisfies a so-called ``quantitative petiteness" condition. The theorem relies on a novel proof of a quantitative Kendall-type theorem which is inspired by the techniques of Markov Chains on general state spaces. We give an application of the technique to the Markov chain approximation of mixing processes.
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