Stéphane Jaffard

Elliptic gaussian random processes.

We study the Gaussian random fields indexed by Rd whose covariance is defined in all generality as the parametrix of an elliptic pseudo-differential operator with minimal regularity assumption on the symbol. We construct new wavelet bases adapted to these operators; the decomposition of the field in this corresponding basis yields its iterated logarithm law and its uniform modulus of continuity. We also characterize the local scalings of the fields in terms of the properties of the principal symbol of the pseudodifferential operator. Similar results are obtained for the Multi-Fractional Brownian Motion.

A simple Wilson orthonormal basis with exponential decay

Following a basic idea of Wilson [“Generalized Wannier functions,” preprint] orthonormal bases for

Wavelet Leaders in Multifractal Analysis

L^2 (\mathbb{R})

Wavelet leaders and bootstrap for multifractal analysis of images

which are a variation on the Gabor scheme are constructed. More precisely,

On the Frisch–Parisi conjecture

\phi \in L^2 (\mathbb{R})

The spectrum of singularities of Riemann's function

is constructed such that the

Identification of filtered white noises

\psi _{ln }

Oscillation spaces: Properties and applications to fractal and multifractal functions

,

Wavelet leader based multifractal analysis

l \in \mathbb{N}

Self-Similar Anisotropic Texture Analysis: The Hyperbolic Wavelet Transform Contribution

,