Multifractal analysis and a-stable processes: A methodological contribution

ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

Volumn 1, Issue , 2000, Pages 241-244

  Chainais, Pierre ^a   Abry, Patrice ^a   Veitch, Darryl ^b  

^a UNIVERSITÉ DE LYON   (France)

^b Software Engineering Research Centre   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

BROWNIAN MOVEMENT; FRACTALS; STABILITY CRITERIA; WAVELET TRANSFORMS; FUNCTIONS; QUEUEING THEORY; REGRESSION ANALYSIS;

ESTIMATION PROCEDURES; FRACTIONAL BROWNIAN MOTION; METHODOLOGICAL CONTRIBUTIONS; MULTI-FRACTAL SPECTRUM; MULTIFRACTAL ANALYSIS; PARTITION FUNCTIONS; SPECIFIC PROPERTIES; WAVELET COEFFICIENTS;

SIGNAL PROCESSING; FRACTALS;

FRACTIONAL BROWNIAN MOTION; LEGENDRE MULTIFRACTAL SPECTRUM; MULTIFRACTAL ANALYSIS; PARTITION FUNCTIONS;

EID: 0033708507     PISSN: 15206149     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICASSP.2000.861930     Document Type: Conference Paper

References (14)

1. P. Abry, P. Flandrin, M.S. Taqqu and D. Veitch. Wavelets for the analysis, estimation and synthesis of scaling data. To appear in Self-Similar Network Traffic and Performance Evaluation, K. Park and W. Will- inger, eds., Wiley Interscience, 1999.
2. P. Abry, L. Delbeke and P. Flandrin, Wavelet-based estimator for the self-similarity parameter of a-stable processes. IEEE-ICASSP-99, Phoenix (AZ), 1999.
3. A. Arneodo, E. Bacry, and J.F. Muzy. Singularity spectrum of fractal signals from wavelet analysis: Exact results. J. Stat. Phys., 70:635-674, 1994.
4. A. Arneodo, J.F. Muzy and E. Bacry. The multifractal formalism revisited with wavelets. Int. J. of Bifurc. and Chaos, 4(2):245-301, 1994.
5. I. Daubechies. Ten lectures on wavelets. SI AM, Philadelphia, Pennsylvania, 1992.
6. L. Delbeke and P. Abry. Stochastic integral representation and properties of the wavelet coefficients of linear fractional stable motion. To appear in Stochastic Processes and their Applications, 1999.
7. S. Jaffard. Multifractal formalism for functions part i: Results valid for all functions. SIAM J. Math. Anal., 28(4):944-970, 1997.
8. W. Feller. An Introduction to Probability Theory and Its Applications, volume 2. John Wiley and Sons, Inc., New-York, London, Sidney, 1962.
9. B. V. Gnedenko and A. N. Kolmogorov. Limit distributions for sums of independent random variables. Addison-Wesley publishing company, Reading, Massachusetts, 1968.
10. P. Gongalvfes and R. H. Riedi. Wavelet analysis of fractional Brownian motion in multifractal time. Proc. 17eme Colloque GRETSI, Vannes, France, 1999.
11. B. Mandelbrot. A multifractal walk down Wall Street. Scientific American, 280:70-73, 1999.
12. B. Pesquet-Popescu. Statistical Properties of the Wavelet Decomposition of Certain Non-Gaussian Self- Similar Processes. To appear IEEE Trans, on Sig. Proc., 1999.
13. R. H. Riedi. Multifractal processes. 1999. preprint.
14. G. Samorodnitsky and M. S. Taqqu. Stable Non- Gaussian Random Processes, stochastic models with infinite variance. Chapman - Hall, New-York, London, 1994.