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
Institut de Mathématique
University of Liège

Research output: Contribution to journal › Article › peer-review

16 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	2101-2116
Number of pages	16
Journal	Nonlinearity
Volume	23
Issue number	9
DOIs	https://doi.org/10.1088/0951-7715/23/9/004
Publication status	Published - 1 Sept 2010
Externally published	Yes

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10.1088/0951-7715/23/9/004

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title = "Some prevalent results about strongly monoH{\"o}lder functions",

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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JO - Nonlinearity

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Some prevalent results about strongly monoHölder functions

Abstract

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