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The Hausdorff spectrum of a class of multifractal processes

Decrouez, Geoffrey, Hambly, Ben and Jones, Owen Dafydd 2015. The Hausdorff spectrum of a class of multifractal processes. Stochastic Processes and their Applications 125 (4) , pp. 1541-1568. 10.1016/j.spa.2014.11.007

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Elsevier
ISSN: 0304-4149
Date of Acceptance: 8 November 2014
Last Modified: 26 Feb 2020 11:45
URI: http://orca.cf.ac.uk/id/eprint/98058

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