From Stochastic Integration w.r.t. Fractional Brownian Motion to Stochastic Integration wrt Multifractional Brownian Motion

Abstract : Because of numerous applications {\textit{e.g.}} in finance and in Internet traffic modelling, stochastic integration w.r.t. fractional Brownian motion (fBm) became a very popular topic in recent years. However, since fBm is not a semi-martingale the Itô integration can not be used for integration w.r.t. fBm and one then needs specific developments. Multifractional Brownian motion (mBm) is a Gaussian process that generalizes fBm by letting the local Hölder exponent vary in time. In addition to the fields mentioned above, it is useful in many and various areas such as geology and biomedicine. In this work we start from the fact, established in \cite[Thm 2.1.(i)]{Herbin Lebovits Vehel}, that an mBm may be approximated, in law, by a sequence of ''tangent" fBms. We used this result to show how one can define a stochastic integral w.r.t. mBm from the stochastic integral w.r.t. fBm, defined in \cite{Bender 2003}, in the white noise theory sense.
Type de document :
Article dans une revue
Annals of the University of Bucharest. Mathematical series, București : Editura Universității din București, 2013
Liste complète des métadonnées

Littérature citée [14 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00818321
Contributeur : Joachim Lebovits <>
Soumis le : vendredi 26 avril 2013 - 15:44:47
Dernière modification le : mardi 30 juillet 2013 - 10:19:20
Document(s) archivé(s) le : mardi 4 avril 2017 - 00:01:36

Fichier

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

Identifiants

  • HAL Id : hal-00818321, version 1

Collections

Citation

Joachim Lebovits. From Stochastic Integration w.r.t. Fractional Brownian Motion to Stochastic Integration wrt Multifractional Brownian Motion. Annals of the University of Bucharest. Mathematical series, București : Editura Universității din București, 2013. 〈hal-00818321〉

Partager

Métriques

Consultations de la notice

103

Téléchargements de fichiers

66