Some prevalent results about strongly monoHölder functions

Marianne Clausel; Samuel Nicolay

doi:10.1088/0951-7715/23/9/004

Some prevalent results about strongly monoHölder functions

Marianne Clausel
, Samuel Nicolay

Université Gustave Eiffel
University of Liège

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

16 Citations (Scopus)

Résumé

We study the typical behaviour of strongly monoHölder functions from the prevalence point of view. To this end we first prove wavelet-based criteria for strongly monoHölder functions. We then use the notion of prevalence to show that the functions of C^α(R^d ) are almost surely strongly monoHölder with Hölder exponent α. Finally, we prove that for any α ∈ (0, 1) on a prevalent set of C ^α(R^d ) the Hausdorff dimension of the graph is equal to d + 1 - α.

langue originale	Anglais
Pages (de - à)	2101-2116
Nombre de pages	16
journal	Nonlinearity
Volume	23
Numéro de publication	9
Les DOIs	https://doi.org/10.1088/0951-7715/23/9/004
état	Publié - 1 sept. 2010
Modification externe	Oui

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abstract = "We study the typical behaviour of strongly monoH{\"o}lder functions from the prevalence point of view. To this end we first prove wavelet-based criteria for strongly monoH{\"o}lder functions. We then use the notion of prevalence to show that the functions of Cα(Rd ) are almost surely strongly monoH{\"o}lder with H{\"o}lder exponent α. Finally, we prove that for any α ∈ (0, 1) on a prevalent set of C α(Rd ) the Hausdorff dimension of the graph is equal to d + 1 - α.",

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AB - We study the typical behaviour of strongly monoHölder functions from the prevalence point of view. To this end we first prove wavelet-based criteria for strongly monoHölder functions. We then use the notion of prevalence to show that the functions of Cα(Rd ) are almost surely strongly monoHölder with Hölder exponent α. Finally, we prove that for any α ∈ (0, 1) on a prevalent set of C α(Rd ) the Hausdorff dimension of the graph is equal to d + 1 - α.

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Some prevalent results about strongly monoHölder functions

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