QUANTITATIVE CONVERGENCE RATES OF MARKOV CHAINS: A SIMPLE ACCOUNT
QUANTITATIVE CONVERGENCE RATES OF MARKOV CHAINS: A SIMPLE ACCOUNT
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马尔可夫链的定量收敛率：一个简单的解释
DOI：
10.1214/ecp.v7-1054
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发表时间：
2002
影响因子：
0.5
通讯作者：
Jeffrey S. Rosenthal
中科院分区：
文献类型：
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作者：
Jeffrey S. Rosenthal
我们陈述并证明了具有不同初始分布但相同转移概率的两个马尔可夫链之间的 k 次迭代后总变异距离的简单定量界限。结果是 Rosenthal (1995) 结果的简化和改进版本，其中还考虑了 Roberts 和 Tweedie (1999) 的 $epsilon$ 改进，并且是 Douc 等人的更复杂的时间非均匀结果的特例。 （2002）。然而，我们提出的证明非常简短；我们认为有必要将证明归结为其本质。本文纯粹是说明性的；没有提出新的结果。
We state and prove a simple quantitative bound on the total variation distance after k iterations between two Markov chains with different initial distributions but identical transition probabilities. The result is a simplified and improved version of the result in Rosenthal (1995), which also takes into account the $epsilon$-improvement of Roberts and Tweedie (1999), and which follows as a special case of the more complicated time-inhomogeneous results of Douc et al. (2002). However, the proof we present is very short and simple; and we feel that it is worthwhile to boil the proof down to its essence. This paper is purely expository; no new results are presented.