Spectral heat content for Lévy processes
| Autor: | Hyunchul Park, Tomasz Grzywny, Renming Song |
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| Rok vydání: | 2018 |
| Předmět: |
Integrable system
Lebesgue measure General Mathematics 010102 general mathematics Mathematical analysis Open set 01 natural sciences Lévy process Measure (mathematics) 010101 applied mathematics 60G51 60J75 35K05 Content (measure theory) Bounded variation Infinitesimal generator 0101 mathematics Mathematics - Probability Mathematics |
| Zdroj: | Mathematische Nachrichten. 292:805-825 |
| ISSN: | 1522-2616 0025-584X |
| Popis: | In this paper we study the spectral heat content for various L\'evy processes. We establish the asymptotic behavior of the spectral heat content for L\'{e}vy processes of bounded variation in $\mathbb{R}^{d}$, $d\geq 1$. We also study the spectral heat content for arbitrary open sets of finite Lebesgue measure in $\mathbb{R}$ with respect to L\'{e}vy processes of unbounded variation under certain conditions on their characteristic exponents. Finally we establish that the asymptotic behavior of the spectral heat content is stable under integrable perturbations to the L\'{e}vy measure. Comment: 19 pages |
| Databáze: | OpenAIRE |
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