Title :

On the monofractality of many stationary continuous Gaussian fields

Author(s) :

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

Journal title :

Journal of Functional Analysis

Pages :

109111

Publisher :

Elsevier

Publication date :

2021-10-01

ISSN :

0022-1236

English keyword(s) :

Sample path behavior
Hölder regularity
spectral density
Besov space
Littlewood-Paley decomposition

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

In this article we focus on a general real-valued continuous stationary Gaussian field X characterized by its spectral density |g| 2 , where g is any even realvalued deterministic square integrable function. Our starting ...
Show more >In this article we focus on a general real-valued continuous stationary Gaussian field X characterized by its spectral density |g| 2 , where g is any even realvalued deterministic square integrable function. Our starting point consists in drawing a close connection between critical Besov regularity of the inverse Fourier transform of g and α X the random pointwise Hölder exponent function of X, which measures local roughness/smoothness of its sample paths at each point. Then, thanks to Littlewood-Paley methods and Hausdorff-Young inequalities, under weak conditions on g, we show that the random function α X is actually a deterministic constant which does not change from point to point. This result means that the field X is of monofractal nature. Also, it is worth mentioning that such a result can easily be extended to the case where X is no longer stationary but has stationary increments.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL