Slow, ordinary and rapid points for Gaussian Wavelets Series and application to Fractional Brownian Motions

Céline Esser; Laurent Loosveldt

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arXiv · 2203.05472

Slow, ordinary and rapid points for Gaussian Wavelets Series and application to Fractional Brownian Motions

Céline Esser·Laurent Loosveldt

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Abstract

We study the H\"olderian regularity of Gaussian wavelets series and show that they display, almost surely, three types of points: slow, ordinary and rapid. In particular, this fact holds for the Fractional Brownian Motion. We also show that this property is satisfied for a multifractal extension of Gaussian wavelet series. Finally, we remark that the existence of slow points is specific to these functions.

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Céline Esser, Laurent Loosveldt. 2022-03-10. Slow, ordinary and rapid points for Gaussian Wavelets Series and application to Fractional Brownian Motions. https://arxiv.org/abs/2203.05472

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