Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motions

Abstract : Stochastic integration w.r.t. fractional Brownian motion (fBm) has raised strong interest in recent years, motivated in particular by applications in finance and Internet traffic modelling. Since fBm is not a semi-martingale, stochastic integration requires specific developments. Multifractional Brownian motion (mBm) generalizes fBm by letting the local Hölder exponent vary in time. This is useful in various areas, including financial modelling and biomedicine. The aim of this work is twofold: first, we prove that an mBm may be approximated in law by a sequence of "tangent" fBms. Second, using this approximation, we show how to construct stochastic integrals w.r.t. mBm by "transporting" corresponding integrals w.r.t. fBm. We illustrate our method on examples such as the Hitsuda-Skohorod and Wick-Itô stochastic integrals.
Type de document :
Article dans une revue
Stochastic Processes and their Applications, Elsevier, 2014, pp.678-708
Liste complète des métadonnées

Littérature citée [26 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00653808
Contributeur : Joachim Lebovits <>
Soumis le : mardi 15 octobre 2013 - 11:53:39
Dernière modification le : jeudi 27 avril 2017 - 09:46:39
Document(s) archivé(s) le : vendredi 7 avril 2017 - 11:09:38

Fichier

Stochastic_Calculus_revised_ve...
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00653808, version 6

Collections

Citation

Joachim Lebovits, Jacques Lévy Véhel, Erick Herbin. Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motions. Stochastic Processes and their Applications, Elsevier, 2014, pp.678-708. 〈hal-00653808v6〉

Partager

Métriques

Consultations de
la notice

613

Téléchargements du document

298