IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v183y2024ics0960077924004867.html
   My bibliography  Save this article

Multifractal analysis of anisotropic and directional pointwise regularities for measures

Author

Listed:
  • Ben Omrane, Ines

Abstract

The usual multifractal analysis for measures studies isotropic pointwise regularity. It does not take into account behaviors that may differ when measured in coordinate axes directions. In this paper, we focus on anisotropic and directional pointwise regularities for Borel probability measures on R2. We will investigate general upper bound results about the dimension prints of the fractal sets of anisotropic regularities and irregularities, and iso-level directional regularity. We apply our results for selfaffine invariant measures on R2 supported by selfaffine Sierpinski Sponges. We show different directional multifractal phenomena. We finally obtain lower bound results about the dimension prints of the fractal sets of anisotropic regularities and irregularities for the measure product of two Borel probability measures on R that have Frostman measures at states q1 and q2 respectively.

Suggested Citation

  • Ben Omrane, Ines, 2024. "Multifractal analysis of anisotropic and directional pointwise regularities for measures," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004867
    DOI: 10.1016/j.chaos.2024.114934
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924004867
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.114934?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Arneodo, A. & Bacry, E. & Muzy, J.F., 1995. "The thermodynamics of fractals revisited with wavelets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 213(1), pages 232-275.
    2. Achour, Rim & Li, Zhiming & Selmi, Bilel & Wang, Tingting, 2024. "A multifractal formalism for new general fractal measures," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    3. DOUZI, Zied & SELMI, Bilel, 2016. "Multifractal variation for projections of measures," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 414-420.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stratimirovic, Djordje & Batas-Bjelic, Ilija & Djurdjevic, Vladimir & Blesic, Suzana, 2021. "Changes in long-term properties and natural cycles of the Danube river level and flow induced by damming," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    2. Makarenko, N.G. & Karimova, L.M. & Kozelov, B.V. & Novak, M.M., 2012. "Multifractal analysis based on the Choquet capacity: Application to solar magnetograms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(18), pages 4290-4301.
    3. Guan, Sihai & Wan, Dongyu & Yang, Yanmiao & Biswal, Bharat, 2022. "Sources of multifractality of the brain rs-fMRI signal," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    4. Pawe{l} O'swik{e}cimka & Stanis{l}aw Dro.zd.z & Mattia Frasca & Robert Gk{e}barowski & Natsue Yoshimura & Luciano Zunino & Ludovico Minati, 2020. "Wavelet-based discrimination of isolated singularities masquerading as multifractals in detrended fluctuation analyses," Papers 2004.03319, arXiv.org.
    5. Ayache, Antoine & Esser, Céline & Kleyntssens, Thomas, 2019. "Different possible behaviors of wavelet leaders of the Brownian motion," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 54-60.
    6. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.
    7. Makowiec, Danuta & Dudkowska, Aleksandra & Gała̧ska, Rafał & Rynkiewicz, Andrzej, 2009. "Multifractal estimates of monofractality in RR-heart series in power spectrum ranges," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3486-3502.
    8. Attia, Najmeddine & Selmi, Bilel, 2023. "On the multifractal measures and dimensions of image measures on a class of Moran sets," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    9. Struzik, Zbigniew R., 2001. "Wavelet methods in (financial) time-series processing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(1), pages 307-319.
    10. Bolzan, M.J.A., 2018. "A modeling substorm dynamics of the magnetosphere using self-organized criticality approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1182-1188.
    11. Wu, Liang & Chen, Lei & Ding, Yiming & Zhao, Tongzhou, 2018. "Testing for the source of multifractality in water level records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 824-839.
    12. Pavlos, G.P. & Iliopoulos, A.C. & Zastenker, G.N. & Zelenyi, L.M. & Karakatsanis, L.P. & Riazantseva, M.O. & Xenakis, M.N. & Pavlos, E.G., 2015. "Tsallis non-extensive statistics and solar wind plasma complexity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 113-135.
    13. Mukli, Peter & Nagy, Zoltan & Eke, Andras, 2015. "Multifractal formalism by enforcing the universal behavior of scaling functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 150-167.
    14. Salat, Hadrien & Murcio, Roberto & Arcaute, Elsa, 2017. "Multifractal methodology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 467-487.
    15. Rodrigues Neto, Camilo & Bube, Kevin & Cser, Adrienn & Otto, Andreas & Feudel, Ulrike, 2004. "Multifractal spectrum of a laser beam melt ablation process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(3), pages 580-586.
    16. Dominique, C-Rene & Rivera-Solis, Luis Eduardo, 2012. "Short-term Dependence in Time Series as an Index of Complexity: Example from the S&P-500 Index," MPRA Paper 41408, University Library of Munich, Germany.
    17. Crepaldi, Antonio F. & Neto, Camilo Rodrigues & Ferreira, Fernando F. & Francisco, Gerson, 2009. "Multifractal regime transition in a modified minority game model," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1364-1371.
    18. Pavlos, G.P. & Malandraki, O.E. & Pavlos, E.G. & Iliopoulos, A.C. & Karakatsanis, L.P., 2016. "Non-extensive statistical analysis of magnetic field during the March 2012 ICME event using a multi-spacecraft approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 149-181.
    19. Morales Martínez, Jorge Luis & Segovia-Domínguez, Ignacio & Rodríguez, Israel Quiros & Horta-Rangel, Francisco Antonio & Sosa-Gómez, Guillermo, 2021. "A modified Multifractal Detrended Fluctuation Analysis (MFDFA) approach for multifractal analysis of precipitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    20. Achour, Rim & Li, Zhiming & Selmi, Bilel & Wang, Tingting, 2024. "A multifractal formalism for new general fractal measures," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004867. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.