论文标题
马尔可夫链的几何达克的等效性
Equivalences of Geometric Ergodicity of Markov Chains
论文作者
论文摘要
本文聚集了不同的条件，这些条件都等同于一般状态空间上时间均匀的马尔可夫链的几何形状真人。总共提出了34个不同的条件（一般链条加7仅用于可逆链），有些旧的和一些新的，例如收敛界限，漂移条件，光谱特性等，对使用的距离度量，功能时刻，初始分布，范围均匀等等，以及更多的假设。提供了不同条件之间连接的证据，主要是独立的，但在适当的情况下使用文献的一些结果。
This paper gathers together different conditions which are all equivalent to geometric ergodicity of time-homogeneous Markov chains on general state spaces. A total of 34 different conditions are presented (27 for general chains plus 7 just for reversible chains), some old and some new, in terms of such notions as convergence bounds, drift conditions, spectral properties, etc., with different assumptions about the distance metric used, finiteness of function moments, initial distribution, uniformity of bounds, and more. Proofs of the connections between the different conditions are provided, mostly self-contained but using some results from the literature where appropriate.
