Strong solutions to singular SDEs and application to the Lennard-Jones potential
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908479211438080 |
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| author | Morale, Daniela Rui, Giulia Ugolini, Stefania |
| author_facet | Morale, Daniela Rui, Giulia Ugolini, Stefania |
| contents | We prove existence and uniqueness of strong solutions to a large class of autonomous stochastic differential equations on an open domain, where the drift exhibits a singular behaviour at the boundary. The main result involves a drift composed of the gradient of a singular potential and an additional possibly singular force. In order to achieve the well-posedness of the model, we employ a probabilistic regularization approach. Under suitable conditions, it is shown that the explosion time of the solution process is infinite. The result is finally applied to the case of an interacting particle system subject to a Lennard-Jones potential, which is singular at the origin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03205 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong solutions to singular SDEs and application to the Lennard-Jones potential Morale, Daniela Rui, Giulia Ugolini, Stefania Probability 60H10, 60H30, 60K35, 60J60, 60J70, 60K40, 82C22, 82C31 We prove existence and uniqueness of strong solutions to a large class of autonomous stochastic differential equations on an open domain, where the drift exhibits a singular behaviour at the boundary. The main result involves a drift composed of the gradient of a singular potential and an additional possibly singular force. In order to achieve the well-posedness of the model, we employ a probabilistic regularization approach. Under suitable conditions, it is shown that the explosion time of the solution process is infinite. The result is finally applied to the case of an interacting particle system subject to a Lennard-Jones potential, which is singular at the origin. |
| title | Strong solutions to singular SDEs and application to the Lennard-Jones potential |
| topic | Probability 60H10, 60H30, 60K35, 60J60, 60J70, 60K40, 82C22, 82C31 |
| url | https://arxiv.org/abs/2508.03205 |