Multidimensional SDE with distributional drift and Lévy noise
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2020
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910494525227008 |
|---|---|
| author | Kremp, Helena Perkowski, Nicolas |
| author_facet | Kremp, Helena Perkowski, Nicolas |
| contents | We solve multidimensional SDEs with distributional drift driven by symmetric, $α$-stable Lévy processes for $α\in (1,2]$ by studying the associated (singular) martingale problem and by solving the Kolmogorov backward equation. We allow for drifts of regularity $(2-2α)/3$, and in particular we go beyond the by now well understood "Young regime", where the drift must have better regularity than $(1-α)/2$. The analysis of the Kolmogorov backward equation in the low regularity regime is based on paracontrolled distributions. As an application of our results we construct a Brox diffusion with Lévy noise.
Keywords: Singular diffusions, stable Lévy noise, distributional drift, paracontrolled distributions, Brox diffusion |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_05222 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Multidimensional SDE with distributional drift and Lévy noise Kremp, Helena Perkowski, Nicolas Probability We solve multidimensional SDEs with distributional drift driven by symmetric, $α$-stable Lévy processes for $α\in (1,2]$ by studying the associated (singular) martingale problem and by solving the Kolmogorov backward equation. We allow for drifts of regularity $(2-2α)/3$, and in particular we go beyond the by now well understood "Young regime", where the drift must have better regularity than $(1-α)/2$. The analysis of the Kolmogorov backward equation in the low regularity regime is based on paracontrolled distributions. As an application of our results we construct a Brox diffusion with Lévy noise. Keywords: Singular diffusions, stable Lévy noise, distributional drift, paracontrolled distributions, Brox diffusion |
| title | Multidimensional SDE with distributional drift and Lévy noise |
| topic | Probability |
| url | https://arxiv.org/abs/2008.05222 |