1D stochastic pressure equation with log-correlated Gaussian coefficients
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918224913760256 |
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| author | Avelin, Benny Kuusi, Tuomo Nummi, Patrik Saksman, Eero Tölle, Jonas M. Viitasaari, Lauri |
| author_facet | Avelin, Benny Kuusi, Tuomo Nummi, Patrik Saksman, Eero Tölle, Jonas M. Viitasaari, Lauri |
| contents | We study unique solvability for one dimensional stochastic pressure equation with diffusion coefficient given by the Wick exponential of log-correlated Gaussian fields. We prove well-posedness for Dirichlet, Neumann and periodic boundary data, and the initial value problem, covering the cases of both the Wick renormalization of the diffusion and of point-wise multiplication. We provide explicit representations for the solutions in both cases, characterized by the $S$-transform and the Gaussian multiplicative chaos measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09127 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 1D stochastic pressure equation with log-correlated Gaussian coefficients Avelin, Benny Kuusi, Tuomo Nummi, Patrik Saksman, Eero Tölle, Jonas M. Viitasaari, Lauri Probability 34F05, 35J57, 46F10, 60G15, 60G57, 60G60, 60H10, 60H40 We study unique solvability for one dimensional stochastic pressure equation with diffusion coefficient given by the Wick exponential of log-correlated Gaussian fields. We prove well-posedness for Dirichlet, Neumann and periodic boundary data, and the initial value problem, covering the cases of both the Wick renormalization of the diffusion and of point-wise multiplication. We provide explicit representations for the solutions in both cases, characterized by the $S$-transform and the Gaussian multiplicative chaos measure. |
| title | 1D stochastic pressure equation with log-correlated Gaussian coefficients |
| topic | Probability 34F05, 35J57, 46F10, 60G15, 60G57, 60G60, 60H10, 60H40 |
| url | https://arxiv.org/abs/2402.09127 |