Approximate factorizations for non-symmetric jump processes
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911126293315584 |
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| author | Cho, Soobin Song, Renming |
| author_facet | Cho, Soobin Song, Renming |
| contents | In this paper, we first extend the approximate factorization for purely discontinuous Markov process established in \cite{CKSV20} by getting rid of some of the conditions imposed in \cite{CKSV20}. Then we apply the approximate factorization to obtain sharp two-sided heat kernel estimates for three classes of processes: stable-like processes with critical killings in $C^{1, {\rm Dini}}$ open sets; killed stable-like processes in the setting of \cite{KW24} in $C^{1, \varepsilon}$ open sets; and non-symmetric stable processes in what we call $C^{1,2{\text - \rm Dini}}$ open sets. In particular, we obtain explicit sharp two-sided heat kernel estimates of killed $α$-stable processes in $C^{1, {\rm Dini}}$ open sets for all $α\in (0, 2)$ and of censored $α$-stable processes in $C^{1, {\rm Dini}}$ open sets for all $α\in (1, 2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14763 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximate factorizations for non-symmetric jump processes Cho, Soobin Song, Renming Probability Analysis of PDEs 60J45, 60J50, 60J76, 47G20, 35K08 In this paper, we first extend the approximate factorization for purely discontinuous Markov process established in \cite{CKSV20} by getting rid of some of the conditions imposed in \cite{CKSV20}. Then we apply the approximate factorization to obtain sharp two-sided heat kernel estimates for three classes of processes: stable-like processes with critical killings in $C^{1, {\rm Dini}}$ open sets; killed stable-like processes in the setting of \cite{KW24} in $C^{1, \varepsilon}$ open sets; and non-symmetric stable processes in what we call $C^{1,2{\text - \rm Dini}}$ open sets. In particular, we obtain explicit sharp two-sided heat kernel estimates of killed $α$-stable processes in $C^{1, {\rm Dini}}$ open sets for all $α\in (0, 2)$ and of censored $α$-stable processes in $C^{1, {\rm Dini}}$ open sets for all $α\in (1, 2)$. |
| title | Approximate factorizations for non-symmetric jump processes |
| topic | Probability Analysis of PDEs 60J45, 60J50, 60J76, 47G20, 35K08 |
| url | https://arxiv.org/abs/2504.14763 |