On the principal eigenvalue for compound Poisson processes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916351994494976 |
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| author | Kim, Daesung Park, Hyunchul |
| author_facet | Kim, Daesung Park, Hyunchul |
| contents | We investigate the explicit expression for the principal eigenvalue $λ_{1}^{X}(D)$ for a large class of compound Poisson processes $X$ on a bounded open set $D$ by examining its spectral heat content. When the jump density of the compound Poisson process is radially symmetric and strictly decreasing, we demonstrate that balls are the unique minimizers for $λ_{1}^{X}(D)$ among all sets with equal Lebesgue measure. Furthermore, we show that this uniqueness fails if the jump density is not strictly decreasing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20571 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the principal eigenvalue for compound Poisson processes Kim, Daesung Park, Hyunchul Probability 60J76 We investigate the explicit expression for the principal eigenvalue $λ_{1}^{X}(D)$ for a large class of compound Poisson processes $X$ on a bounded open set $D$ by examining its spectral heat content. When the jump density of the compound Poisson process is radially symmetric and strictly decreasing, we demonstrate that balls are the unique minimizers for $λ_{1}^{X}(D)$ among all sets with equal Lebesgue measure. Furthermore, we show that this uniqueness fails if the jump density is not strictly decreasing. |
| title | On the principal eigenvalue for compound Poisson processes |
| topic | Probability 60J76 |
| url | https://arxiv.org/abs/2405.20571 |