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On the Multifractal Analysis of the Branching Random Walk in $$\mathbb{R }^d$$ R d

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  • Najmeddine Attia

    (Domaine de Volucceau)

Abstract

We establish the almost sure validity of the multifractal formalism for $$\mathbb{R }^d$$ R d -valued branching random walks on the whole relative interior of the natural convex domain of study.

Suggested Citation

  • Najmeddine Attia, 2014. "On the Multifractal Analysis of the Branching Random Walk in $$\mathbb{R }^d$$ R d," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1329-1349, December.
    • Handle: RePEc:spr:jotpro:v:27:y:2014:i:4:d:10.1007_s10959-013-0488-x
    DOI: 10.1007/s10959-013-0488-x
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    References listed on IDEAS

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    1. Julien Barral, 2000. "Continuity of the Multifractal Spectrum of a Random Statistically Self-Similar Measure," Journal of Theoretical Probability, Springer, vol. 13(4), pages 1027-1060, October.
    2. Liu, Quansheng, 2000. "On generalized multiplicative cascades," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 263-286, April.
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    Cited by:

    1. Xiaoqiang Wang & Chunmao Huang, 2017. "Convergence of Martingale and Moderate Deviations for a Branching Random Walk with a Random Environment in Time," Journal of Theoretical Probability, Springer, vol. 30(3), pages 961-995, September.
    2. Najmeddine Attia, 2021. "On the Multifractal Analysis of Branching Random Walk on Galton–Watson Tree with Random Metric," Journal of Theoretical Probability, Springer, vol. 34(1), pages 90-102, March.
    3. Mahjoub, Amal & Attia, Najmeddine, 2022. "A relative vectorial multifractal formalism," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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