Asymptotic behavior of densities of unimodal convolution semigroups. (English) Zbl 1370.60060
Authors’ abstract: We prove the asymptotic formulas for the densities of isotropic unimodal convolution semigroups of probability measures on \(\mathbb{R}^{d}\) under the assumption that its Lévy-Khintchine exponent is regularly varying of index between \(0\) and \(2\).
Reviewer: Marius Iosifescu (Bucureşti)
MSC:
| 60F99 | Limit theorems in probability theory |
| 60J75 | Jump processes (MSC2010) |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 60G51 | Processes with independent increments; Lévy processes |
| 60J65 | Brownian motion |
| 44A10 | Laplace transform |
| 46F12 | Integral transforms in distribution spaces |
Keywords:
unimodal convolution semigroups; densities; asymptotic formula; Lévy-Khintchine exponent; heat kernel; Green function; isotropic unimodal Lévy process; subordinate Brownian motionReferences:
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