Titre :

On local path behavior of Surgailis multifractional processes

Auteur(s) :

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

Titre de la revue :

Theory of Probability and Mathematical Statistics

Éditeur :

American Mathematical Society

Date de publication :

2022

ISSN :

0094-9000

Mot(s)-clé(s) en anglais :

Gaussian processes
variable Hurst parameter
local and pointwise Hölder regularity
local self-similarity

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

Multifractional processes are stochastic processes with non-stationary increments whose local regularity and self-similarity properties change from point to point. The paradigmatic example of them is the classical ...
Lire la suite >Multifractional processes are stochastic processes with non-stationary increments whose local regularity and self-similarity properties change from point to point. The paradigmatic example of them is the classical Multifractional Brownian Motions (MBM) {M(t)} t∈R of Benassi, Jaffard, Lévy Véhel, Peltier and Roux, which was constructed in the mid 90's just by replacing the constant Hurst parameter H of the well-known Fractional Brownian Motion by a deterministic function H(t) having some smoothness. More then 10 years later, using a different construction method, which basically relies on nonhomogeneous fractional integration and differentiation operators, Surgailis introduced two non-classical Gaussian multifactional processes denoted by {X(t)} t∈R and {Y (t)} t∈R. In our article, under a rather weak condition on the functional parameter H(•), we show that {M(t)} t∈R and {X(t)} t∈R as well as {M(t)} t∈R and {Y (t)} t∈R only differ by a part which is locally more regular than {M(t)} t∈R itself. Thus it turns out that the two non-classical multifractional processes {X(t)} t∈R and {Y (t)} t∈R have exactly the same local path behavior as that of the classical MBM {M(t)} t∈R .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 :

2025-01-24T16:17:55Z