Weak error for SDEs with additive stable noise and singular drift: choose the test function in the same space as the drift!
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910156994904064 |
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| author | Jourdain, Benjamin Menozzi, Stéphane |
| author_facet | Jourdain, Benjamin Menozzi, Stéphane |
| contents | We emphasize that for a stochastic differential equation with isotropic stable additive noise and non Lipschitz drift, when considering an appropriate discretization scheme and the associated weak error, it is somehow natural to consider a test function having the same spatial regularity as the drift involved. We will in particular focus on drifts belonging to Lebsegue, H{ö}lder or Besov spaces with negative regularity index in their spatial variable. Choosing such a test function allows to improve the convergence rate previously obtained on the densities (for Lebesgue or H{ö}lder drifts) or preserve the rate for possibly singular generalized test functions (for Besov spaces with negative regularity). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20323 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weak error for SDEs with additive stable noise and singular drift: choose the test function in the same space as the drift! Jourdain, Benjamin Menozzi, Stéphane Probability We emphasize that for a stochastic differential equation with isotropic stable additive noise and non Lipschitz drift, when considering an appropriate discretization scheme and the associated weak error, it is somehow natural to consider a test function having the same spatial regularity as the drift involved. We will in particular focus on drifts belonging to Lebsegue, H{ö}lder or Besov spaces with negative regularity index in their spatial variable. Choosing such a test function allows to improve the convergence rate previously obtained on the densities (for Lebesgue or H{ö}lder drifts) or preserve the rate for possibly singular generalized test functions (for Besov spaces with negative regularity). |
| title | Weak error for SDEs with additive stable noise and singular drift: choose the test function in the same space as the drift! |
| topic | Probability |
| url | https://arxiv.org/abs/2604.20323 |