Survival probability for jump processes in unbounded domains on metric measure spaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915470022541312 |
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| author | Mariano, Phanuel Wang, Jing |
| author_facet | Mariano, Phanuel Wang, Jing |
| contents | We study the large time behavior of the survival probability $\mathbb{P}_x\left(τ_D>t\right)$ for symmetric jump processes in unbounded domains with a positive bottom of the spectrum. We prove asymptotic upper and lower bounds with explicit constants in terms of the bottom of the spectrum $λ(D)$. Our main result applies to symmetric jump processes in general metric measure spaces. For $α$-stable processes in unbounded uniformly $C^{1,1}$ domains, our results provide a probabilistic interpretation and an equivalent geometric condition for $λ(D)>0$. In the case of increasing horn-shaped domains, the exponential rate of decay for the survival probability is sharp. We also present examples of unbounded domains where our results apply. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21158 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Survival probability for jump processes in unbounded domains on metric measure spaces Mariano, Phanuel Wang, Jing Probability Analysis of PDEs Spectral Theory We study the large time behavior of the survival probability $\mathbb{P}_x\left(τ_D>t\right)$ for symmetric jump processes in unbounded domains with a positive bottom of the spectrum. We prove asymptotic upper and lower bounds with explicit constants in terms of the bottom of the spectrum $λ(D)$. Our main result applies to symmetric jump processes in general metric measure spaces. For $α$-stable processes in unbounded uniformly $C^{1,1}$ domains, our results provide a probabilistic interpretation and an equivalent geometric condition for $λ(D)>0$. In the case of increasing horn-shaped domains, the exponential rate of decay for the survival probability is sharp. We also present examples of unbounded domains where our results apply. |
| title | Survival probability for jump processes in unbounded domains on metric measure spaces |
| topic | Probability Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2508.21158 |