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Wavelet analysis of the multivariate fractional brownian motion

Jean-François CoeurjollyPierre-Olivier AmblardSophie Achard — 2013

ESAIM: Probability and Statistics

The work developed in the paper concerns the multivariate fractional Brownian motion (mfBm) viewed through the lens of the wavelet transform. After recalling some basic properties on the mfBm, we calculate the correlation structure of its wavelet transform. We particularly study the asymptotic behaviour of the correlation, showing that if the analyzing wavelet has a sufficient number of null first order moments, the decomposition eliminates any possible long-range (inter)dependence. The cross-spectral...

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