Sample path properties of parabolic SPDEs with non constant coefficients
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913858819457024 |
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| author | Dalang, Robert C. Sanz-Solé, Marta |
| author_facet | Dalang, Robert C. Sanz-Solé, Marta |
| contents | We consider an SPDE driven by a parabolic second order partial differential operator with a nonlinear random external forcing defined by a Gaussian noise that is white in time and has a spatially homogeneous covariance. We prove existence and uniqueness of a random field solution to this SPDE. Our main result concerns the space-time sample path regularity of its solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23995 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sample path properties of parabolic SPDEs with non constant coefficients Dalang, Robert C. Sanz-Solé, Marta Probability Primary 60H15, Secondary 60H20, 60G60, 60G15 We consider an SPDE driven by a parabolic second order partial differential operator with a nonlinear random external forcing defined by a Gaussian noise that is white in time and has a spatially homogeneous covariance. We prove existence and uniqueness of a random field solution to this SPDE. Our main result concerns the space-time sample path regularity of its solution. |
| title | Sample path properties of parabolic SPDEs with non constant coefficients |
| topic | Probability Primary 60H15, Secondary 60H20, 60G60, 60G15 |
| url | https://arxiv.org/abs/2410.23995 |