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A joint multifractal analysis of vector valued non Gibbs measures

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  • Menceur, Mohamed
  • Mabrouk, Anouar Ben

Abstract

The multifractal formalism for measures holds whenever the existence of corresponding Gibbs-like measures supported on the singularities sets holds. In the present work we tried to relax such a hypothesis and introduce a more general framework of joint multifractal analysis where the measures constructed on the singularities sets are not Gibbs but controlled by an extra-function allowing the multifractal formalism to hold. We fall on the classical case by a particular choice of such a function. An answer to a question raised in [2] on which gauge function φ shall we get a finite, infinite or zero value of Hμ,φq,t(K) for the singularities set K is provided.

Suggested Citation

  • Menceur, Mohamed & Mabrouk, Anouar Ben, 2019. "A joint multifractal analysis of vector valued non Gibbs measures," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 203-217.
    • Handle: RePEc:eee:chsofr:v:126:y:2019:i:c:p:203-217
    DOI: 10.1016/j.chaos.2019.05.010
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    1. Ben Mabrouk, Anouar, 2008. "A higher order multifractal formalism," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1412-1421, September.
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    Cited by:

    1. Wang, Jian & Shao, Wei & Kim, Junseok, 2020. "Multifractal detrended cross-correlation analysis between respiratory diseases and haze in South Korea," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Mahjoub, Amal & Attia, Najmeddine, 2022. "A relative vectorial multifractal formalism," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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