Geodesic
Wavelet analysis of the multivariate fractional brownian motion
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 592-604

Voir la notice de l'article provenant de la source Numdam

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 density is also considered in a second part. Its existence is proved and its evaluation is performed using a von Bahr-Essen like representation of the function sign(t)|t|α. The behaviour of the cross-spectral density of the wavelet field at the zero frequency is also developed and confirms the results provided by the asymptotic analysis of the correlation.

DOI : 10.1051/ps/2012011
Classification : 26A16, 28A80, 42C40
Keywords: multivariate fractional brownian motion, wavelet analysis, cross-correlation, cross-spectrum 
@article{PS_2013__17__592_0,
     author = {Coeurjolly, Jean-Fran\c{c}ois and Amblard, Pierre-Olivier and Achard, Sophie},
     title = {Wavelet analysis of the multivariate fractional brownian motion},
     journal = {ESAIM: Probability and Statistics},
     pages = {592--604},
     publisher = {EDP-Sciences},
     volume = {17},
     year = {2013},
     doi = {10.1051/ps/2012011},
     mrnumber = {3085634},
     zbl = {1293.42038},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2012011/}
}
TY  - JOUR
AU  - Coeurjolly, Jean-François
AU  - Amblard, Pierre-Olivier
AU  - Achard, Sophie
TI  - Wavelet analysis of the multivariate fractional brownian motion
JO  - ESAIM: Probability and Statistics
PY  - 2013
SP  - 592
EP  - 604
VL  - 17
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ps/2012011/
DO  - 10.1051/ps/2012011
LA  - en
ID  - PS_2013__17__592_0
ER  - 
%0 Journal Article
%A Coeurjolly, Jean-François
%A Amblard, Pierre-Olivier
%A Achard, Sophie
%T Wavelet analysis of the multivariate fractional brownian motion
%J ESAIM: Probability and Statistics
%D 2013
%P 592-604
%V 17
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ps/2012011/
%R 10.1051/ps/2012011
%G en
%F PS_2013__17__592_0
Coeurjolly, Jean-François; Amblard, Pierre-Olivier; Achard, Sophie. Wavelet analysis of the multivariate fractional brownian motion. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 592-604. doi: 10.1051/ps/2012011

Cité par Sources :