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6 Result(s)

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  1. No Access

    Article

    Wavelet eigenvalue regression in high dimensions

    In this paper, we construct the wavelet eigenvalue regression methodology (Abry and Didier in J Multivar Anal 168:75–104, 2018a; in Bernoulli 24(2):895–928, 2018b) in high dimensions. We assume that possibly n...

    Patrice Abry, B. Cooper Boniece… in Statistical Inference for Stochastic Proce… (2023)

  2. No Access

    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...

    Patrice Abry, Stéphane Jaffard… in Recent Developments in Fractals and Relate… (2017)

  3. No Access

    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...

    Patrice Abry, Stéphane Jaffard, Roberto Leonarduzzi… in Fractal Geometry and Stochastics V (2015)

  4. No Access

    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)...

    Béatrice Vedel, Herwig Wendt, Patrice Abry… in Dependence in Probability and Statistics (2010)

  5. No Access

    Article

    Second order properties of distribution tails and estimation of tail exponents in random difference equations

    According to a celebrated result of Kesten (Acta Math 131:207–248, 1973), random difference equations have a power-law distribution tail in the asymptotic sense. Empirical evidence shows that classical estimators...

    Changryong Baek, Vladas Pipiras, Herwig Wendt, Patrice Abry in Extremes (2009)

  6. No Access

    Chapter and Conference Paper

    Wavelet Decomposition of Measures: Application to Multifractal Analysis of Images

    We show the relevance of multifractal analysis for some problems in image processing. We relate it to the standard question of the determination of correct function space settings. We show why a scale-invarian...

    Patrice Abry, Stéphane Jaffard… in Unexploded Ordnance Detection and Mitigati… (2009)