Bernstein's inequality for general Markov chains

Bai Jiang Qiang Sun Jianqing Fan

Statistics Theory and Methods mathscidoc:1912.43410

arXiv preprint arXiv:1805.10721, 2018.5
We prove a sharp Bernstein inequality for general-state-space and not necessarily reversible Markov chains. It is sharp in the sense that the variance proxy term is optimal. Our result covers the classical Bernstein's inequality for independent random variables as a special case.
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@inproceedings{bai2018bernstein's,
  title={Bernstein's inequality for general Markov chains},
  author={Bai Jiang, Qiang Sun, and Jianqing Fan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114244578503970},
  booktitle={arXiv preprint arXiv:1805.10721},
  year={2018},
}
Bai Jiang, Qiang Sun, and Jianqing Fan. Bernstein's inequality for general Markov chains. 2018. In arXiv preprint arXiv:1805.10721. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114244578503970.
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