Dirichlet heat kernel estimates for rectilinear stable processes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909597160177664 |
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| author | Chen, Zhen-Qing Hu, Eryan Zhao, Guohuan |
| author_facet | Chen, Zhen-Qing Hu, Eryan Zhao, Guohuan |
| contents | Let $d \geq 2$, $α\in (0,2)$, and $X$ be the rectilinear $α$-stable process on $\mathbb{R}^d$. We first present a geometric characterization of an open subset $D\subset \mathbb{R}^d$ so that the part process $X^D$ of $X$ in $D$ is irreducible. We then study the properties of the transition density functions of $X^D$, including the strict positivity property as well as their sharp two-sided bounds in $C^{1,1}$ domains in $\mathbb{R}^d$. Our bounds are shown to be sharp for a class of $C^{1,1}$ domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14026 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dirichlet heat kernel estimates for rectilinear stable processes Chen, Zhen-Qing Hu, Eryan Zhao, Guohuan Probability Let $d \geq 2$, $α\in (0,2)$, and $X$ be the rectilinear $α$-stable process on $\mathbb{R}^d$. We first present a geometric characterization of an open subset $D\subset \mathbb{R}^d$ so that the part process $X^D$ of $X$ in $D$ is irreducible. We then study the properties of the transition density functions of $X^D$, including the strict positivity property as well as their sharp two-sided bounds in $C^{1,1}$ domains in $\mathbb{R}^d$. Our bounds are shown to be sharp for a class of $C^{1,1}$ domains. |
| title | Dirichlet heat kernel estimates for rectilinear stable processes |
| topic | Probability |
| url | https://arxiv.org/abs/2304.14026 |