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

La loi d'entrée de la mesure des excursions du processus réfléchi pour certaines classes de processus de Lévy

Loïc Chaumont (1) , Jacek Małecki (2)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
2 Wroclaw University of Science and Technology

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.

Domaines: Probabilités [math.PR]

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