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On Fractional Brownian Motion and Wavelets
Journal article   Peer reviewed

On Fractional Brownian Motion and Wavelets

S Albeverio, P Jorgensen and A Paolucci
Complex Analysis and Operator Theory, Vol.6(1), pp.33-63
02/2012
DOI: 10.1007/s11785-010-0077-2

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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.
Mathematics q -Fractional Brownian motion 60G22 Hilbert spaces Cuntz algebras 46C05 Wavelets Operator Theory Filters 42C40 Analysis 47L90 Mathematics, general Fractional Brownian motion

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