Journal article
On Fractional Brownian Motion and Wavelets
Complex Analysis and Operator Theory, Vol.6(1), pp.33-63
02/2012
DOI: 10.1007/s11785-010-0077-2
Abstract
Given a fractional Brownian motion (fBm) with Hurst index $${H\in(0,1)}$$ , we associate with this a special family of representations of Cuntz algebras related to frequency domains and wavelets. Vice versa, we consider a pair of Haar wavelets satisfying some compatibility conditions, and we construct the covariance functions of fBm with a fixed Hurst index. The Cuntz algebra representations enter the picture as filters of the associated wavelets. Extensions to q-dependent covariance functions leading to a corresponding fBm process will also be discussed.
Details
- Title: Subtitle
- On Fractional Brownian Motion and Wavelets
- Creators
- S Albeverio - ACC. ARCH (USI) Lugano SwitzerlandP Jorgensen - Mathematics Department University of Iowa Iowa City IA 52242 USAA Paolucci - Max-Planck-Institut für Mathematik Vivatsgasse 7 53111 Bonn Germany
- Resource Type
- Journal article
- Publication Details
- Complex Analysis and Operator Theory, Vol.6(1), pp.33-63
- DOI
- 10.1007/s11785-010-0077-2
- ISSN
- 1661-8254
- eISSN
- 1661-8262
- Publisher
- SP Birkhäuser Verlag Basel; Basel
- Language
- English
- Date published
- 02/2012
- Academic Unit
- Mathematics
- Record Identifier
- 9983985931302771
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