Lacunary wavelet series on Cantor sets
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866911905670496256 |
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| author | Esser, Céline Vedel, Béatrice |
| author_facet | Esser, Céline Vedel, Béatrice |
| contents | We provide a multifractal analysis of lacunary wavelet series on Cantor sets. Byintroducing a desynchronization between the scales of the wavelets and the scales of the steps of the construction of the Cantor set, we obtain random processes that donot satisfy multifractal formalisms based on the Legendre transform and on the large deviation of wavelet leaders. Subsequently, we show how the computation of the leader large deviation spectra of "lacunarized" versions of such wavelet series can detect the failure in the multifractal formalism using only numerical quantities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_03733 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Lacunary wavelet series on Cantor sets Esser, Céline Vedel, Béatrice Probability Functional Analysis 42C40, 28A80, 26A16, 60G17 We provide a multifractal analysis of lacunary wavelet series on Cantor sets. Byintroducing a desynchronization between the scales of the wavelets and the scales of the steps of the construction of the Cantor set, we obtain random processes that donot satisfy multifractal formalisms based on the Legendre transform and on the large deviation of wavelet leaders. Subsequently, we show how the computation of the leader large deviation spectra of "lacunarized" versions of such wavelet series can detect the failure in the multifractal formalism using only numerical quantities. |
| title | Lacunary wavelet series on Cantor sets |
| topic | Probability Functional Analysis 42C40, 28A80, 26A16, 60G17 |
| url | https://arxiv.org/abs/2207.03733 |