Heat kernel estimates for kinetic SDEs with drifts being unbounded and in Kato's class
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929223427424256 |
|---|---|
| author | Ren, Chongyang Zhang, Xicheng |
| author_facet | Ren, Chongyang Zhang, Xicheng |
| contents | In this paper we investigate the existence and uniqueness of weak solutions for kinetic stochastic differential equations with Hölder diffusion and unbounded singular drifts in Kato's class. Moreover, we also establish sharp two-sided estimates for the density of the solution. In particular, the drift $b$ can be in the mixed $L^q_tL^{p_1}_{x_1}L^{p_2}_{x_2}$ space with $\frac2q+\frac{d}{p_1}+\frac{3d}{p_2}<1$. As an application, we show the existence and uniqueness of weak solution to a second order singular interacting particle system in ${\mathbb R}^{d N}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Heat kernel estimates for kinetic SDEs with drifts being unbounded and in Kato's class Ren, Chongyang Zhang, Xicheng Probability 60H10 In this paper we investigate the existence and uniqueness of weak solutions for kinetic stochastic differential equations with Hölder diffusion and unbounded singular drifts in Kato's class. Moreover, we also establish sharp two-sided estimates for the density of the solution. In particular, the drift $b$ can be in the mixed $L^q_tL^{p_1}_{x_1}L^{p_2}_{x_2}$ space with $\frac2q+\frac{d}{p_1}+\frac{3d}{p_2}<1$. As an application, we show the existence and uniqueness of weak solution to a second order singular interacting particle system in ${\mathbb R}^{d N}$. |
| title | Heat kernel estimates for kinetic SDEs with drifts being unbounded and in Kato's class |
| topic | Probability 60H10 |
| url | https://arxiv.org/abs/2401.13873 |