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Grenoble Images Parole Signal Automatique |
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Grenoble Images Parole Signal Automatique |
| HAL: hal-00501720, version 2 |
| arXiv: 1007.2109 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2010-07-13) | v2 (2011-06-30) |
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| Wavelet analysis of the multivariate fractional Brownian motion |
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| Jean-François Coeurjolly 1, 2Pierre-Olivier Amblard 1 |
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| (2010-07-10) |
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| 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 behavior 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 $\sign(t) |t|^\alpha$. The behavior 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. |
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| 1: | Grenoble Images Parole Signal Automatique (GIPSA-lab) |
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CNRS : UMR5216 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Université Stendhal - Grenoble III – Institut Polytechnique de Grenoble - Grenoble Institute of Technology |
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| 2: | Laboratoire Jean Kuntzmann (LJK) |
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CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre-Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology |
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| Subject | : | Mathematics/Statistics Statistics/Statistics Theory Engineering Sciences/Signal and Image processing Computer Science/Signal and Image Processing |
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| multivariate fractional Brownian motion – cross-covariance – cross-spectral density – wavelet analysis |
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| hal-00501720, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00501720 | |
| oai:hal.archives-ouvertes.fr:hal-00501720 | |
| From: Jean-François Coeurjolly | |
| Submitted on: Thursday, 30 June 2011 11:16:52 | |
| Updated on: Thursday, 30 June 2011 13:36:46 | |
