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References (56)
-
Xiaochuan Yang (2015)
Multifractality of jump diffusion processesAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
-
J. Aubry, F. Bastin, S. Dispa, S. Jaffard (2007)
The S\nu spaces: new spaces defined with wavelet coefficients and related to multifractal analysisInternational journal of applied mathematics and statistics, 7
-
U. Frisch (1980)
FULLY DEVELOPED TURBULENCE AND INTERMITTENCYAnnals of the New York Academy of Sciences, 357
-
A. Fraysse, S. Jaffard (2006)
How smooth is almost every function in a Sobolev spaceRevista Matematica Iberoamericana, 22
-
S. Mazurkiewicz (1931)
Sur les fonctions non dérivablesStudia Mathematica, 3
-
Z. Buczolich, S. Seuret (2013)
Measures and functions with prescribed homogeneous multifractal spectrumarXiv: Classical Analysis and ODEs
-
A. Fraysse (2010)
Regularity criteria for almost every function in Sobolev spacesJournal of Functional Analysis, 258
-
JM Aubry (2013)
631J. Func. Anal., 264
-
Z. Buczolich, S. Seuret (2011)
MULTIFRACTAL SPECTRUM AND GENERIC PROPERTIES OF FUNCTIONS MONOTONE IN SEVERAL VARIABLESJournal of Mathematical Analysis and Applications, 382
-
S. Jaffard (2004)
Wavelet Techniques in Multifractal Analysis -
Z. Buczolich, S. Seuret (2017)
Multifractal properties of typical convex functionsMonatshefte für Mathematik, 187
-
M. Ghil, R. Benzi, G. Parisi, Società Fisica (1985)
Turbulence and predictability in geophysical fluid dynamics and climate dynamics -
A Ayache (2007)
327Rev. Mat. Iberoamericana, 23
-
V. Gruslys, Julius Jonušas, V. Mijovic, O. Ng, Lars Olsen, I. Petrykiewicz (2012)
Dimensions of prevalent continuous functionsMonatshefte für Mathematik, 166
-
Delphine Maman, S. Seuret (2016)
Fixed Points for the Multifractal Spectrum MapConstructive Approximation, 43
-
A. Ayache, S. Jaffard, M. Taqqu (2007)
Wavelet construction of Generalized Multifractional processes.Revista Matematica Iberoamericana, 23
-
P. Abry, H. Wendt, S. Jaffard (2013)
When Van Gogh meets Mandelbrot: Multifractal classification of painting's textureSignal Process., 93
-
F. Bayart (2012)
Multifractal spectra of typical and prevalent measuresNonlinearity, 26
-
(1997)
Solutions multifractales de l’´equation de burgers -
A SURVEY ON PRESCRIPTION OF MULTIFRACTAL BEHAVIOR -
(1990)
Ondelettes et opérateurs I. Hermann -
(1974)
Multiplications aléatoires itérées et distributions invariantes par moyennes pondérées -
Z. Buczolich, S. Seuret (2010)
Typical Borel measures on [0, 1]d satisfy a multifractal formalismNonlinearity, 23
-
L. Olsen (2010)
Prevalent Lq-dimensions of measuresMathematical Proceedings of the Cambridge Philosophical Society, 149
-
S. Banach (1931)
Über die Baire'sche Kategorie gewisser FunktionenmengenStudia Mathematica, 3
-
R. Leonarduzzi, P. Abry, S. Jaffard, H. Wendt, Lucie Gournay, Tita Kyriacopoulou, Claude Martineau, Cristian Martinez (2017)
P-leader multifractal analysis for text type identification2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
-
JM Aubry (2007)
82Int. J. Appl. Math. Statist., 7
-
Z. Buczolich, J. Nagy (1999)
Hölder Spectrum of Typical Monotone Continuous FunctionsReal analysis exchange, 26
-
B. Lashermes, S. Roux, P. Abry, S. Jaffard (2008)
Comprehensive multifractal analysis of turbulent velocity using the wavelet leadersThe European Physical Journal B, 61
-
(2007)
and Murad S -
Given an admissible (homogeneous or not) singularity spectrum σ : R + → [0 , d ] ∪ {−∞} , is there a functional space in which Baire typical functions -
J. Aubry, Delphine Maman, S. Seuret (2010)
Local behavior of traces of Besov functions: Prevalent resultsarXiv: Functional Analysis
-
S Banach (1931)
174Studia Math., 3
-
H. Hentschel, I. Procaccia (1983)
The infinite number of generalized dimensions of fractals and strange attractorsPhysica D: Nonlinear Phenomena, 8
-
J Barral (2005)
589J. Fourier Anal. Appl., 11
-
J. Barral (2015)
Inverse problems in multifractal analysis of measuresAnnales Scientifiques De L Ecole Normale Superieure, 48
-
J Barral (2015)
1457Ann. Ec. Norm. Sup, 48
-
J. Muzy, E. Bacry, A. Arneodo (1993)
Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method.Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 47 2
-
(1989)
Exposants de Hölder en des points donnés et coefficients d’ondelettes -
J. Barral, S. Seuret (2020)
Besov spaces in multifractal environment and the Frisch-Parisi conjecture -
T. Halsey, M. Jensen, L. Kadanoff, I. Procaccia, B. Shraiman (1986)
Erratum: Fractal measures and their singularities: The characterization of strange setsPhysical review. A, General physics, 34 2
-
L. Olsen (2010)
Fractal and multifractal dimensions of prevalent meausuresIndiana University Mathematics Journal, 59
-
Stéphane Jaffard (1992)
Construction de fonctions multifractales ayant un spectre de singularités prescrit, 315
-
I. Daubechies (1992)
Ten Lectures on WaveletsComputers in Physics, 6
-
J. Barral, S. Seuret (2005)
From Multifractal Measures to Multifractal Wavelet SeriesJournal of Fourier Analysis and Applications, 11
-
Z. Buczolich, S. Seuret (2011)
HÖLDER SPECTRUM OF FUNCTIONS MONOTONE IN SEVERAL VARIABLES -
A. Fraysse, Stéphane Jaffard, J. Kahane (2005)
Quelques propriétés génériques en analyseComptes Rendus Mathematique, 340
-
T. Halsey, M. Jensen, L. Kadanoff, I. Procaccia, B. Shraiman (1987)
Fractal measures and their singularities: The characterization of strange sets.Physical review. A, General physics, 33 2
-
G. Brown, G. Michon, J. Peyriére (1992)
On the multifractal analysis of measuresJournal of Statistical Physics, 66
-
P Abry (2015)
31 -
P. Abry, S. Jaffard, H. Wendt (2012)
Irregularities and Scaling in Signal and Image Processing: Multifractal AnalysisarXiv: Functional Analysis
-
P Abry (2013)
554Signal Process., 93
-
J. Barral, N. Fournier, S. Jaffard, S. Seuret (2009)
A pure jump Markov process with a random singularity spectrumarXiv: Probability
-
S. Jaffard (2000)
On the Frisch–Parisi conjectureJournal de Mathématiques Pures et Appliquées, 79
-
S. Jaffard (1995)
Functions with Prescribed Hölder ExponentApplied and Computational Harmonic Analysis, 2
-
L. Olsen (1995)
A Multifractal FormalismAdvances in Mathematics, 116
- Publisher
- Springer International Publishing
- Copyright
- © Springer Nature Switzerland AG 2021
- ISBN
- 978-3-030-59648-4
- Pages
- 47 –70
- DOI
- 10.1007/978-3-030-59649-1_3
- Publisher site
- See Chapter on Publisher Site
Abstract
[Multifractal behavior has been identified and mathematically established for large classes of functions, stochastic processes and measures. Multifractality has also been observed on many data coming from Geophysics, turbulence, Physics, Biology, to name a few. Developing mathematical models whose scaling and multifractal properties fit those measured on data is thus an important issue. This raises several still unsolved theoretical questions about the prescription of multifractality (i.e. how to build mathematical models with a singularity spectrum known in advance), typical behavior in function spaces, and existence of solutions to PDEs or SPDEs with possible multifractal behavior. In this survey, we gather some of the latest results in this area.]
Published: Mar 24, 2021
Keywords: Hausdorff measure and dimension; Fractals and multifractals; Hölder; Sobolev and Besov spaces; Wavelets; Baire category and spaces; 11K55; 26A21; 28AXX; 42C40; 46E35