Almost Sure Hausdorff
Dimension of Graphs of
Random Wavelet Series |
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Authors: | Email author" target="_blank">Fran?ois?RoueffEmail author |
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Institution: | (1) Ecole Nationale Supérieure des Télécommunications CNRS URA 820, 46, rue Barrault, 75634 Paris, Cedex 13, France |
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Abstract: | In this contribution, we consider the problem of computing the Hausdorff dimension
of the graph of a continuous random field obtained as an infinite series of smooth deterministic
functions with independent random weights. The particular case of random wavelet series is
addressed and almost sure lower bounds of their Hausdorff dimension are obtained. Sub-classes
are exhibited for which these lower bounds coincide with almost sure upper bounds based on
particular smoothness indices of the series. A direct application of these results provides new
insights concerning the Hausdorff dimension as opposed to classical smoothness indices. |
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Keywords: | |
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