ASYMPTOTICS IN SMALL TIME FOR THE DENSITY OF A STOCHASTIC DIFFERENTIAL EQUATION DRIVEN BY A STABLE LEVY PROCESS

Abstract : This work focuses on the asymptotic behavior of the density in small time of a stochastic differential equation driven by an α-stable process with index α ∈ (0, 2). We assume that the process depends on a parameter β = (θ, σ) T and we study the sensitivity of the density with respect to this parameter. This extends the results of [5] which was restricted to the index α ∈ (1, 2) and considered only the sensitivity with respect to the drift coefficient. By using Malliavin calculus, we obtain the representation of the density and its derivative as an expectation and a conditional expectation. This permits to analyze the asymptotic behavior in small time of the density, using the time rescaling property of the stable process. MSC2010: 60G51; 60G52; 60H07; 60H20; 60H10; 60J75.
Type de document :
Pré-publication, Document de travail
2017
Liste complète des métadonnées

Littérature citée [14 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01410989
Contributeur : Emmanuelle Clément <>
Soumis le : mercredi 8 novembre 2017 - 16:20:54
Dernière modification le : vendredi 10 novembre 2017 - 01:15:38

Fichier

densityRev-06-11-17.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01410989, version 2

Citation

Emmanuelle Clément, Arnaud Gloter, Huong Nguyen. ASYMPTOTICS IN SMALL TIME FOR THE DENSITY OF A STOCHASTIC DIFFERENTIAL EQUATION DRIVEN BY A STABLE LEVY PROCESS. 2017. 〈hal-01410989v2〉

Partager

Métriques

Consultations de la notice

71

Téléchargements de fichiers

6