A new Multifractional Process with Random Exponent

Ayache, Antoine; Esser, Céline; Hamonier, Julien

Type de document :

Article dans une revue scientifique: Article original

URL permanente :

http://hdl.handle.net/20.500.12210/121979

Titre :

A new Multifractional Process with Random Exponent

Auteur(s) :

Ayache, Antoine [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Esser, Céline [Auteur]
Hamonier, Julien [Auteur]

Titre de la revue :

Risk and Decision Analysis

Éditeur :

IOS

Date de publication :

2018

ISSN :

1569-7371

Mot(s)-clé(s) en anglais :

Fractional Brownian Motion
varying Hurst parameter
Haar basis
Hölder regularity
Itô integral

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

A first type of Multifractional Process with Random Exponent (MPRE) was constructed several years ago in [2] by replacing in a wavelet series representation of Fractional Brownian Motion (FBM) the Hurst parameter by a ...
Lire la suite >A first type of Multifractional Process with Random Exponent (MPRE) was constructed several years ago in [2] by replacing in a wavelet series representation of Fractional Brownian Motion (FBM) the Hurst parameter by a random variable depending on the time variable. In the present article, we propose another approach for constructing another type of MPRE. It consists in substituting to the Hurst parameter, in a stochastic integral representation of the high-frequency part of FBM, a random variable depending on the integration variable. The MPRE obtained in this way offers, among other things, the advantages to have a representation through classical Itô integral and to be less difficult to simulate than the first type of MPRE, previously introduced in [2]. Yet, the study of Hölder regularity of this new MPRE is a significantly more challenging problem than in the case of the previous one. Actually, it requires to develop a new methodology relying on an extensive use of the Haar basis.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T14:53:44Z

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