On the monofractality of many stationary ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
On the monofractality of many stationary continuous Gaussian fields
Author(s) :
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
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 >
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
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