Density behaviour related to Lévy processes - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2020

Density behaviour related to Lévy processes


Let p t (x), f t (x) and q * t (x) be the densities at time t of a real Lévy process, its running supremum and the entrance law of the reflected excursions at the infimum. We provide relationships between the asymptotic behaviour of p t (x), f t (x) and q * t (x), when t is small and x is large. Then for large x, these asymptotic behaviours are compared to this of the density of the Lévy measure. We show in particular that, under mild conditions, if p t (x) is comparable to tν(x), as t → 0 and x → ∞, then so is f t (x).
Fichier principal
Vignette du fichier
cm4.pdf (508.35 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02433327 , version 1 (09-01-2020)


  • HAL Id : hal-02433327 , version 1


Loïc Chaumont, Jacek Małecki. Density behaviour related to Lévy processes. 2020. ⟨hal-02433327⟩
28 View
42 Download


Gmail Facebook X LinkedIn More