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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.13788 |
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| _version_ | 1866917843595952128 |
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| author | Qian, Bin Zhang, Beibei |
| author_facet | Qian, Bin Zhang, Beibei |
| contents | In this paper, we obtain the reverse Bakry-Émery type estimates for a class of hypoelliptic diffusion operator by coupling method. The (right and reverse) Poincaré inequalities and the (right and reverse) logarithmic Sobolev inequalities are presented as consequences of such estimates. Wang-Harnack inequality, Hamilton's gradient estimate and Liouville property are also presented by reverse logarithmic Sobolev inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13788 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling Qian, Bin Zhang, Beibei Probability 60J60, 35H10 In this paper, we obtain the reverse Bakry-Émery type estimates for a class of hypoelliptic diffusion operator by coupling method. The (right and reverse) Poincaré inequalities and the (right and reverse) logarithmic Sobolev inequalities are presented as consequences of such estimates. Wang-Harnack inequality, Hamilton's gradient estimate and Liouville property are also presented by reverse logarithmic Sobolev inequality. |
| title | Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling |
| topic | Probability 60J60, 35H10 |
| url | https://arxiv.org/abs/2411.13788 |