A new Multifractional Process with Random Exponent

Ayache, Antoine; Esser, Céline; Hamonier, Julien

Document type :

Article dans une revue scientifique: Article original

Permalink :

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

Title :

A new Multifractional Process with Random Exponent

Author(s) :

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

Journal title :

Risk and Decision Analysis

Publisher :

IOS

Publication date :

2018

ISSN :

1569-7371

English keyword(s) :

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

HAL domain(s) :

Mathématiques [math]

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T14:53:44Z

Files

document
Open access
Access the document

PaperAyacheEsserHamonier.pdf
Open access
Access the document

A new Multifractional Process with Random Exponent BibTeX CSV Excel RIS

Files

A new Multifractional Process with Random Exponent

BibTeX

CSV

Excel

RIS