Free Access
Issue
ESAIM: PS
Volume 16, 2012
Page(s) 352 - 374
DOI https://doi.org/10.1051/ps/2010014
Published online 01 August 2012
  1. A. Ayache and J. Lévy-Véhel, Generalized Multifractional Brownian Motion : definition and preliminary results, in Fractals Theory and applications in engineering, edited by M. Dekking, J. Lévy-Véhel, E. Lutton and C. Tricot. Springer (1999) 17–32. [Google Scholar]
  2. J.M. Bardet and P. Bertrand, Definition, properties and wavelets analysis of Multiscale Fractional Brownian Motion. Fractals 15 (2007) 73–87. [CrossRef] [Google Scholar]
  3. J.M. Bardet, G. Lang, G. Oppenheim, A. Phillipe, S. Stoev and M.S. Taqqu, Generators of long-range dependent processes : A survey, in Theory and Applications of Long Range Dependance, edited by P. Doukhan M. Oppenheim and G. Taqqu. Birkäuser (2003) 579–623. [Google Scholar]
  4. M. Basseville and I. Nikiforov, Detection of abrupt changes–Theory and applications. Prentice-Hall (1993). [Google Scholar]
  5. A. Benassi and S. Deguy, Multi-scale Fractional Motion : definition and identification, Preprint LAIC (1999). [Google Scholar]
  6. A. Benassi, S. Jaffard and D. Roux, Elliptic Gaussian random processes. Revista Matematica Iberoamericana 13 (1997) 19–90. [CrossRef] [MathSciNet] [Google Scholar]
  7. J. Beran, Statistics for Long-Memory processes. Chapman and Hall, London, UK (1994). [Google Scholar]
  8. Z. Ciesielski, G. Kerkyacharian and B. Roynette, Quelques espaces fonctionnels associés à des processus Gaussiens. Stud. Math. 107 (1993). [Google Scholar]
  9. M. Clausel, More about uniform irregularity : the wavelet point of view. Preprint (2008). [Google Scholar]
  10. J.J. Collins and C.J. De Luca, Open loop and closed loop control of posture : a random walk analysis of center of pressure trajectories, Exp. Brain Res. 9 (1993) 308–318. [CrossRef] [PubMed] [Google Scholar]
  11. H. Csörgö and L. Horvath, Non parametric method for change point problems in Handbook of statistics, edited by P.R. Krishnaiah and C.R. Rao. Elsevier, New York 7 (1988) 403–425. [Google Scholar]
  12. R.B. Davies and D.S. Harte, Tests for Hurst effect. Biometrika 74 (1987) 95–101. [CrossRef] [Google Scholar]
  13. C.R. Dietrich and G.N. Newsam, Fast and exact simulation of stationary Gaussian processes through circulant embedding of the covariance matrix. SIAM J. Sci. Comput. 18 (1997) 1088–1107. [CrossRef] [MathSciNet] [Google Scholar]
  14. K. Falconer, Fractal Geometry. John Wiley and Sons (1990). [Google Scholar]
  15. K. Falconer, Tangent Fields and the local structure of random fields. J. Theor. Prob. 15 (2002) 731–750. [CrossRef] [MathSciNet] [Google Scholar]
  16. K. Falconer, The local structure of random processes. J. London Math. Soc. 67 (2003) 657–672. [CrossRef] [MathSciNet] [Google Scholar]
  17. U. Frisch, Turbulence, the legacy of A.N. Kolmogorov. Cambridge University Press (1995). [Google Scholar]
  18. J.P. Kahane, Geza Freud and lacunary Fourier series. J. Approx. Theory 46 (1986) 51–57. [CrossRef] [MathSciNet] [Google Scholar]
  19. I. Karatzas and S.E. Shreve, Brownian Motion and stochastic calculus. Springer-Verlag (1988). [Google Scholar]
  20. A.N. Kolmogorov, Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum. C. R. Acad. Sci. URSS 26 (1940) 115–118. [Google Scholar]
  21. J. Lévy-Vehel and R.F. Peltier, Multifractional Brownian Motion : definition and preliminary results, Rapport de recherche de l’INRIA n° 2645 (1995). [Google Scholar]
  22. S. Mallat, A wavelet tour of signal processing. Academic Press (1998). [Google Scholar]
  23. Y. Meyer, Ondelettes et opérateurs. Hermann (1990). [Google Scholar]
  24. Y. Meyer, F. Sellan and M.S. Taqqu, Wavelets, generalized white noise and fractional integration : the synthesis of Fractional Brownian Motion. J. Fourier Anal. Appl. 5 (1999) 465–494. [CrossRef] [MathSciNet] [Google Scholar]
  25. B.M. Mandelbrot and J. Van Ness, Fractional Brownian Motion, fractional noises and applications. SIAM Rev. 10 (1968) 422–437. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  26. W. Willinger, M.S. Taqqu and V. Teverosky, Stock market price and long-range dependence. Finance and Stochastics 1 (1999) 1–14. [CrossRef] [Google Scholar]
  27. A.T.A. Wood and G. Chan, Simulation of stationary Gaussian processes in [ 0;1 ] d. J. Comput. Graph. Stat. 3 (1994) 409–432. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.