IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v183y2024ics0960077924004521.html
   My bibliography  Save this article

On Lp rectangular multifractal multivariate functions

Author

Listed:
  • Ben Slimane, Mourad
  • Alzughaibi, Imtithal
  • Algahtani, Obaid

Abstract

Multifractal analysis has traditionally been based on the pointwise Hölder regularity for locally bounded functions. However, recently an extension to the rectangular pointwise regularity for multivariate locally functions has generated interest. The purpose of this paper is twofold. Firstly, we characterize in hyperbolic wavelet bases the rectangular pointwise Lipschitz regularity for multivariate functions which are non necessarily locally bounded but are locally in Lp. Secondly, we perform applications for both random and deterministic anisotropic self-affine tools for some models of textures in images and flows in turbulence. Actually, we show that fractional anisotropic Wiener field are multivariate monofractal in Lp. We then construct self-affine cascade functions that are multivariate multifractal in Lp.

Suggested Citation

  • Ben Slimane, Mourad & Alzughaibi, Imtithal & Algahtani, Obaid, 2024. "On Lp rectangular multifractal multivariate functions," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004521
    DOI: 10.1016/j.chaos.2024.114900
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924004521
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.114900?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. S. Davies & P. Hall, 1999. "Fractal analysis of surface roughness by using spatial data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 3-37.
    2. Biermé, Hermine & Meerschaert, Mark M. & Scheffler, Hans-Peter, 2007. "Operator scaling stable random fields," Stochastic Processes and their Applications, Elsevier, vol. 117(3), pages 312-332, March.
    3. Mourad Ben Slimane & Moez Ben Abid & Ines Ben Omrane & Mohamad Maamoun Turkawi, 2020. "Pointwise Rectangular Lipschitz Regularities for Fractional Brownian Sheets and Some Sierpinski Selfsimilar Functions," Mathematics, MDPI, vol. 8(7), pages 1-18, July.
    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. Sönmez, Ercan, 2018. "The Hausdorff dimension of multivariate operator-self-similar Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 426-444.
    2. Wu, Dongsheng & Xiao, Yimin, 2009. "Continuity in the Hurst index of the local times of anisotropic Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1823-1844, June.
    3. Li, Yuqiang & Xiao, Yimin, 2011. "Multivariate operator-self-similar random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1178-1200, June.
    4. Lim, C.Y. & Meerschaert, M.M. & Scheffler, H.-P., 2014. "Parameter estimation for operator scaling random fields," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 172-183.
    5. Sun, Ying & Chang, Xiaohui & Guan, Yongtao, 2018. "Flexible and efficient estimating equations for variogram estimation," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 45-58.
    6. Gneiting, Tilmann, 2002. "Compactly Supported Correlation Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 493-508, November.
    7. Kristoufek, Ladislav & Vosvrda, Miloslav, 2014. "Commodity futures and market efficiency," Energy Economics, Elsevier, vol. 42(C), pages 50-57.
    8. Alina Bărbulescu & Cristian Ștefan Dumitriu, 2023. "Fractal Characterization of Brass Corrosion in Cavitation Field in Seawater," Sustainability, MDPI, vol. 15(4), pages 1-14, February.
    9. Mikkel Bennedsen, 2016. "Semiparametric inference on the fractal index of Gaussian and conditionally Gaussian time series data," CREATES Research Papers 2016-21, Department of Economics and Business Economics, Aarhus University.
    10. Lee, Jeonghwa, 2021. "Hurst estimation for operator scaling random fields," Statistics & Probability Letters, Elsevier, vol. 178(C).
    11. Finlay, Richard & Seneta, Eugene, 2017. "A scalar-valued infinitely divisible random field with Pólya autocorrelation," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 141-146.
    12. Guo, Hongwen & Lim, Chae Young & Meerschaert, Mark M., 2009. "Local Whittle estimator for anisotropic random fields," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 993-1028, May.
    13. Puplinskaitė, Donata & Surgailis, Donatas, 2015. "Scaling transition for long-range dependent Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2256-2271.
    14. Kremer, D. & Scheffler, H.-P., 2019. "Operator-stable and operator-self-similar random fields," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4082-4107.
    15. Biermé, Hermine & Lacaux, Céline & Scheffler, Hans-Peter, 2011. "Multi-operator scaling random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2642-2677, November.
    16. Li, Ming & Li, Jia-Yue, 2017. "Generalized Cauchy model of sea level fluctuations with long-range dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 309-335.
    17. Abry, Patrice & Didier, Gustavo, 2018. "Wavelet eigenvalue regression for n-variate operator fractional Brownian motion," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 75-104.
    18. Patrice Abry & Gustavo Didier & Hui Li, 2019. "Two-step wavelet-based estimation for Gaussian mixed fractional processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 157-185, July.
    19. George P. Papaioannou & Christos Dikaiakos & Akylas C. Stratigakos & Panos C. Papageorgiou & Konstantinos F. Krommydas, 2019. "Testing the Efficiency of Electricity Markets Using a New Composite Measure Based on Nonlinear TS Tools," Energies, MDPI, vol. 12(4), pages 1-30, February.
    20. Taghreed Alghamdi & Khalid Elgazzar & Taysseer Sharaf, 2021. "Spatiotemporal Traffic Prediction Using Hierarchical Bayesian Modeling," Future Internet, MDPI, vol. 13(9), pages 1-18, August.

    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:s0960077924004521. 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.