Chernoff-type bound for finite Markov chains
Chernoff-type bound for finite Markov chains
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DOI：
10.1214/aoap/1028903453
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发表时间：
1998-08
影响因子：
1.8
通讯作者：
P. Lezaud
中科院分区：
文献类型：
--
作者：
P. Lezaud
本文给出了不可约有限状态马尔可夫链经验均值分布函数的界。D. Gillman，减少了这个问题的边界的最大特征值的扰动的转移矩阵的马尔可夫链。利用Kato在《线性算子的扰动理论》一书中给出的特征值估计，我们简化了D. Gillman推广到不可逆有限状态马尔可夫链和连续时间。我们还提出了另一种方法，直接适用于一些一般的遍历马尔可夫核具有谱间隙。
This paper develops bounds on the distribution function of the empirical mean for irreducible finite-state Markov chains. One approach, explored by D. Gillman, reduces this problem to bounding the largest eigenvalue of a perturbation of the transition matrix for the Markov chain. By using estimates on eigenvalues given in Kato's book ''Perturbation Theory for Linear Operators'', we simplify the proof of D. Gillman and extend it to non-reversible finite-state Markov chains and continuous time. We also set out another method, directly applicable to some general ergodic Markov kernels having a spectral gap.