Weak well-posedness and weak discretization error for stable-driven SDEs with Lebesgue drift
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916245766406144 |
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| author | Fitoussi, Mathis Jourdain, Benjamin Menozzi, Stéphane |
| author_facet | Fitoussi, Mathis Jourdain, Benjamin Menozzi, Stéphane |
| contents | We are interested in the discretization of stable driven SDEs with additive noise for $α$ $\in$ (1, 2) and Lq -- Lp drift under the Serrin type condition $α$/q + d/p < $α$ -- 1. We show weak existence and uniqueness as well as heat kernel estimates for the SDE and obtain a convergence rate of order (1/$α$)*($α$ -- 1 -- $α$/q - d/p) for the difference of the densities for the Euler scheme approximation involving suitably cutoffed and time randomized drifts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak well-posedness and weak discretization error for stable-driven SDEs with Lebesgue drift Fitoussi, Mathis Jourdain, Benjamin Menozzi, Stéphane Probability We are interested in the discretization of stable driven SDEs with additive noise for $α$ $\in$ (1, 2) and Lq -- Lp drift under the Serrin type condition $α$/q + d/p < $α$ -- 1. We show weak existence and uniqueness as well as heat kernel estimates for the SDE and obtain a convergence rate of order (1/$α$)*($α$ -- 1 -- $α$/q - d/p) for the difference of the densities for the Euler scheme approximation involving suitably cutoffed and time randomized drifts. |
| title | Weak well-posedness and weak discretization error for stable-driven SDEs with Lebesgue drift |
| topic | Probability |
| url | https://arxiv.org/abs/2405.08378 |