The Hausdorff spectrum of a class of multifractal processes

Decrouez, Geoffrey, Hambly, Ben and Jones, Owen Dafydd ORCID: https://orcid.org/0000-0002-7300-5510 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:	02 Nov 2022 10:16
URI:	https://orca.cardiff.ac.uk/id/eprint/98058

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