Bernstein-type Inequalities for Markov Chains and Markov Processes: A Simple and Robust Proof
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916991131975680 |
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| author | Huang, De Li, Xiangyuan |
| author_facet | Huang, De Li, Xiangyuan |
| contents | We establish a new Bernstein-type deviation inequality for general (non-reversible) discrete-time Markov chains via an elementary approach. More robust than existing works in the literature, our result only requires the Markov chain to satisfy an iterated Poincaré inequality. Moreover, our method can be readily generalized to continuous-time Markov processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04930 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bernstein-type Inequalities for Markov Chains and Markov Processes: A Simple and Robust Proof Huang, De Li, Xiangyuan Probability 60J05, 60J25, 37A30 We establish a new Bernstein-type deviation inequality for general (non-reversible) discrete-time Markov chains via an elementary approach. More robust than existing works in the literature, our result only requires the Markov chain to satisfy an iterated Poincaré inequality. Moreover, our method can be readily generalized to continuous-time Markov processes. |
| title | Bernstein-type Inequalities for Markov Chains and Markov Processes: A Simple and Robust Proof |
| topic | Probability 60J05, 60J25, 37A30 |
| url | https://arxiv.org/abs/2408.04930 |