Quantitative heat kernel estimates for diffusions with distributional drift
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| Acceso en línea: | |
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| _version_ | 1866913120388120576 |
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| author | Perkowski, Nicolas van Zuijlen, Willem |
| author_facet | Perkowski, Nicolas van Zuijlen, Willem |
| contents | We consider the stochastic differential equation on $\mathbb{R}^d$ given by $$ \, \mathrm{d}X_t = b(t,X_t) \, \mathrm{d}t + \, \mathrm{d} B_t, $$ where $B$ is a Brownian motion and $b$ is considered to be a distribution of regularity $ > -\frac12$. We show that the martingale solution of the SDE has a transition kernel $Γ_t$ and prove upper and lower heat kernel bounds for $Γ_t$ with explicit dependence on $t$ and the norm of $b$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_10786 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Quantitative heat kernel estimates for diffusions with distributional drift Perkowski, Nicolas van Zuijlen, Willem Probability We consider the stochastic differential equation on $\mathbb{R}^d$ given by $$ \, \mathrm{d}X_t = b(t,X_t) \, \mathrm{d}t + \, \mathrm{d} B_t, $$ where $B$ is a Brownian motion and $b$ is considered to be a distribution of regularity $ > -\frac12$. We show that the martingale solution of the SDE has a transition kernel $Γ_t$ and prove upper and lower heat kernel bounds for $Γ_t$ with explicit dependence on $t$ and the norm of $b$. |
| title | Quantitative heat kernel estimates for diffusions with distributional drift |
| topic | Probability |
| url | https://arxiv.org/abs/2009.10786 |