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The Hausdorff spectrum of a class of multifractal processes

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  • Decrouez, Geoffrey
  • Hambly, Ben
  • Jones, Owen Dafydd

Abstract

The Multifractal Embedded Branching Process (MEBP) process and Canonical Embedded Branching Process (CEBP) process were introduced by Decrouez and Jones (2012). The CEBP is a process in which the crossings of dyadic intervals constitute a branching process. An MEBP process is defined as a multifractal time-change of a CEBP process, where the time-change is such that both it and the CEBP can be simulated on-line. In this paper, under various moment conditions, we show that CEBP processes have a constant modulus of continuity, obtain the Hausdorff spectrum of the time-change, and thus obtain the Hausdorff spectrum of an MEBP process.

Suggested Citation

  • Decrouez, Geoffrey & Hambly, Ben & Jones, Owen Dafydd, 2015. "The Hausdorff spectrum of a class of multifractal processes," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1541-1568.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:4:p:1541-1568
    DOI: 10.1016/j.spa.2014.11.007
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    References listed on IDEAS

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    3. Iksanov, Aleksander M., 2004. "Elementary fixed points of the BRW smoothing transforms with infinite number of summands," Stochastic Processes and their Applications, Elsevier, vol. 114(1), pages 27-50, November.
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