Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

The entrance law of the excursion measure of the reflected process for some classes of Lévy processes

Abstract : We provide integral formulae for the Laplace transform of the entrance law of the reflected excursions for symmetric Lévy processes in terms of their characteristic exponent. For subordinate Brownian motions and stable processes we express the density of the entrance law in terms of the generalized eigenfunctions for the semigroup of the process killed when exiting the positive half-line. We use the formulae to study in-depth properties of the density of the entrance law such as asymptotic behavior of its derivatives in time variable.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [19 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02121758
Contributor : Loïc Chaumont Connect in order to contact the contributor
Submitted on : Monday, May 6, 2019 - 5:33:46 PM
Last modification on : Wednesday, October 27, 2021 - 1:23:29 PM
Long-term archiving on: : Wednesday, October 2, 2019 - 4:30:09 AM

File

cm3.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02121758, version 1

Collections

`

Citation

Loïc Chaumont, Jacek Małecki. The entrance law of the excursion measure of the reflected process for some classes of Lévy processes. 2019. ⟨hal-02121758⟩

Share

Metrics

Record views

77

Files downloads

114