Title :

Moving average Multifractional Processes with Random Exponent: lower bounds for local oscillations

Author(s) :

Ayache, Antoine [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Bouly, Florent [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Stochastic Processes and their Applications

Publisher :

Elsevier

Publication date :

2022-04

ISSN :

0304-4149

English keyword(s) :

Fractional Brownian Motion
varying Hurst parameter
pointwise Hölder regularity
Itô integral

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

In the last few years Ayache, Esser and Hamonier introduced a new Multifractional Process with Random Exponent (MPRE) obtained by replacing the Hurst parameter in a moving average representation of Fractional Brownian ...
Show more >In the last few years Ayache, Esser and Hamonier introduced a new Multifractional Process with Random Exponent (MPRE) obtained by replacing the Hurst parameter in a moving average representation of Fractional Brownian Motion through Wiener integral by an adapted Hölder continuous stochastic process indexed by the integration variable. Thus, this MPRE can be expressed as a moving average Itô integral which is a considerable advantage with respect to another MPRE introduced a long time ago by Ayache and Taqqu. Thanks to this advantage, very recently, Loboda, Mies and Steland have derived interesting results on local Hölder regularity, self-similarity and other properties of the recently introduced moving average MPRE and generalizations of it. Yet, the problem of obtaining, on an universal event of probability 1 not depending on the location, relevant lower bounds for local oscillations of such processes has remained open. We solve it in the present article under some conditions.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL