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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.26439 |
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| _version_ | 1866917550157201408 |
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| author | Liu, Ziyu Xiang, Shengquan |
| author_facet | Liu, Ziyu Xiang, Shengquan |
| contents | This note studies the 1D stochastic heat equation driven by a one-dimensional Brownian motion. We prove that the associated Markov process satisfies the strong Feller property under mild non-degeneracy conditions. The approach combines Malliavin calculus with the moment method from PDE control theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26439 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on the strong Feller property via the moment method Liu, Ziyu Xiang, Shengquan Probability This note studies the 1D stochastic heat equation driven by a one-dimensional Brownian motion. We prove that the associated Markov process satisfies the strong Feller property under mild non-degeneracy conditions. The approach combines Malliavin calculus with the moment method from PDE control theory. |
| title | A note on the strong Feller property via the moment method |
| topic | Probability |
| url | https://arxiv.org/abs/2605.26439 |