论文标题
在Lyapunov Foster Criterion和Poincaré不平等的Markov连锁店
On the Lyapunov Foster criterion and Poincaré inequality for Reversible Markov Chains
论文作者
论文摘要
本文提出了从寄养 - 莱帕诺夫漂移条件开始的离散时间可逆的马尔可夫链的随机稳定性的基本证明。除了其相对简单性外，证明还有两个显着特征：（i）它完全依赖于功能分析的非稳定参数； （ii）它使福斯特 - 莱帕诺夫功能与庞加莱不平等之间的联系显式。该证明用于得出光谱间隙的显式结合。还提出了非可逆情况的扩展。
This paper presents an elementary proof of stochastic stability of a discrete-time reversible Markov chain starting from a Foster-Lyapunov drift condition. Besides its relative simplicity, there are two salient features of the proof: (i) it relies entirely on functional-analytic non-probabilistic arguments; and (ii) it makes explicit the connection between a Foster-Lyapunov function and Poincaré inequality. The proof is used to derive an explicit bound for the spectral gap. An extension to the non-reversible case is also presented.
