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.
  2. J.M. Bardet and P. Bertrand, Definition, properties and wavelets analysis of Multiscale Fractional Brownian Motion. Fractals 15 (2007) 73–87. [CrossRef]
  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.
  4. M. Basseville and I. Nikiforov, Detection of abrupt changes–Theory and applications. Prentice-Hall (1993).
  5. A. Benassi and S. Deguy, Multi-scale Fractional Motion : definition and identification, Preprint LAIC (1999).
  6. A. Benassi, S. Jaffard and D. Roux, Elliptic Gaussian random processes. Revista Matematica Iberoamericana 13 (1997) 19–90. [CrossRef] [MathSciNet]
  7. J. Beran, Statistics for Long-Memory processes. Chapman and Hall, London, UK (1994).
  8. Z. Ciesielski, G. Kerkyacharian and B. Roynette, Quelques espaces fonctionnels associés à des processus Gaussiens. Stud. Math. 107 (1993).
  9. M. Clausel, More about uniform irregularity : the wavelet point of view. Preprint (2008).
  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]
  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.
  12. R.B. Davies and D.S. Harte, Tests for Hurst effect. Biometrika 74 (1987) 95–101. [CrossRef]
  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]
  14. K. Falconer, Fractal Geometry. John Wiley and Sons (1990).
  15. K. Falconer, Tangent Fields and the local structure of random fields. J. Theor. Prob. 15 (2002) 731–750. [CrossRef] [MathSciNet]
  16. K. Falconer, The local structure of random processes. J. London Math. Soc. 67 (2003) 657–672. [CrossRef] [MathSciNet]
  17. U. Frisch, Turbulence, the legacy of A.N. Kolmogorov. Cambridge University Press (1995).
  18. J.P. Kahane, Geza Freud and lacunary Fourier series. J. Approx. Theory 46 (1986) 51–57. [CrossRef] [MathSciNet]
  19. I. Karatzas and S.E. Shreve, Brownian Motion and stochastic calculus. Springer-Verlag (1988).
  20. A.N. Kolmogorov, Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum. C. R. Acad. Sci. URSS 26 (1940) 115–118.
  21. J. Lévy-Vehel and R.F. Peltier, Multifractional Brownian Motion : definition and preliminary results, Rapport de recherche de l’INRIA n° 2645 (1995).
  22. S. Mallat, A wavelet tour of signal processing. Academic Press (1998).
  23. Y. Meyer, Ondelettes et opérateurs. Hermann (1990).
  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]
  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]
  26. W. Willinger, M.S. Taqqu and V. Teverosky, Stock market price and long-range dependence. Finance and Stochastics 1 (1999) 1–14. [CrossRef]
  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.

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.