HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Density behaviour related to Lévy processes

Abstract : 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).
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [18 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02433327
Contributor : Loïc Chaumont Connect in order to contact the contributor
Submitted on : Thursday, January 9, 2020 - 9:12:48 AM
Last modification on : Wednesday, November 3, 2021 - 9:15:28 AM
Long-term archiving on: : Saturday, April 11, 2020 - 12:15:10 PM

File

cm4.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02433327, version 1

Collections

Citation

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

Share

Metrics

Record views

28

Files downloads

23