The Hausdorff spectrum of a class of multifractal processes

Geoffrey Decrouez, Ben Hambly and Owen Dafydd Jones

Stochastic Processes and their Applications, 2015, vol. 125, issue 4, 1541-1568

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.

Keywords: Multifractal processes; Hausdorff spectrum; Multifractal spectrum; Singularity spectrum; Branching processes (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spa.2014.11.007

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