8 Result(s)
within
Stéphane Jaffard
Probability Theory and Stochastic Processes
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Chapter and Conference Paper
New Exponents for Pointwise Singularity Classification
We introduce new tools for pointwise singularity classification: We investigate the properties of the two-variable function which is defined at every point as the p-exponent of a fractional integral of order t; n...
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Chapter and Conference Paper
Multifractal Analysis Based on p-Exponents and Lacunarity Exponents
Many examples of signals and images cannot be modeled by locally bounded functions, so that the standard multifractal analysis, based on the Hölder exponent, is not feasible. We present a multifractal analysis...
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Chapter
Multivariate Davenport Series
We consider series of the form ∑a n {n ⋅x}, where n ∈ Z d and {x} is the sawtooth function. They are the natural multivar...
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Article
Multifractal analysis of Lévy fields
We study the pointwise regularity properties of the Lévy fields introduced by T. Mori; these fields are the most natural generalization of Lévy processes to the multivariate setting. We determine their spectru...
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Chapter
Space-Filling Functions and Davenport Series
In this paper, we study the pointwise Hölder regularity of some spacefilling functions. In particular, we give some general results concerning the pointwise regularity of the Davenport series.
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Chapter
On the impact of the number of vanishing moments on the dependence structures of compound Poisson motion and fractional Brownian motion in multifractal time
From a theoretical perspective, scale invariance, or simply scaling, can fruitfully be modeled with classes of multifractal stochastic processes, designed from positive multiplicative martingales (or cascades)...
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Article
The multifractal nature of Lévy processes
We show that the sample paths of most Lévy processes are multifractal functions and we determine their spectrum of singularities.
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Chapter
Wavelets and analysis of partial differential equations
We describe the main properties of decompositions in orthonormal bases of wavelets. We then apply them to the theoretical and numerical study of some partial differential equations.
