A unified approach to the small-time behavior of the spectral heat content for isotropic Lévy processes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913247246942208 |
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| author | Kobayashi, Kei Park, Hyunchul |
| author_facet | Kobayashi, Kei Park, Hyunchul |
| contents | This paper establishes the precise small-time asymptotic behavior of the spectral heat content for isotropic Lévy processes on bounded $C^{1,1}$ open sets of $\mathbb{R}^{d}$ with $d\ge 2$, where the underlying characteristic exponents are regularly varying at infinity with index $α\in (1,2]$, including the case $α=2$. Moreover, this asymptotic behavior is shown to be stable under an integrable perturbation of its Lévy measure. These results cover a wide class of isotropic Lévy processes, including Brownian motions, stable processes, and jump diffusions, and the proofs provide a unified approach to the asymptotic behavior of the spectral heat content for all of these processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11690 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A unified approach to the small-time behavior of the spectral heat content for isotropic Lévy processes Kobayashi, Kei Park, Hyunchul Probability This paper establishes the precise small-time asymptotic behavior of the spectral heat content for isotropic Lévy processes on bounded $C^{1,1}$ open sets of $\mathbb{R}^{d}$ with $d\ge 2$, where the underlying characteristic exponents are regularly varying at infinity with index $α\in (1,2]$, including the case $α=2$. Moreover, this asymptotic behavior is shown to be stable under an integrable perturbation of its Lévy measure. These results cover a wide class of isotropic Lévy processes, including Brownian motions, stable processes, and jump diffusions, and the proofs provide a unified approach to the asymptotic behavior of the spectral heat content for all of these processes. |
| title | A unified approach to the small-time behavior of the spectral heat content for isotropic Lévy processes |
| topic | Probability |
| url | https://arxiv.org/abs/2306.11690 |