Free Access
Volume 12, April 2008
Page(s) 30 - 50
Published online 13 November 2007
  1. P. Abry and F. Sellan, The wavelet-based synthesis for fractional Brownian motion proposed by F. Sellan and Y. Meyer: remarks and fast implementation. Appl. Comput. Harmon. Anal. 3 (1996) 377–383. [CrossRef] [MathSciNet] [Google Scholar]
  2. A. Ayache, A. Bonami and A. Estrade, Identification and series decomposition of anisotropic Gaussian fields. Proceedings of the Catania ISAAC05 congress (2005). [Google Scholar]
  3. J.M. Bardet, G. Lang, G. Oppenheim, A. Philippe, S. Stoev and M.S. Taqqu, Semi-parametric estimation of the long-range dependence parameter: a survey. In Theory and applications of long-range dependence, Birkhäuser Boston (2003) 557–577. [Google Scholar]
  4. A. Begyn, Asymptotic development and central limit theorem for quadratic variations of gaussian processes. To appear in Bernoulli (2006). [Google Scholar]
  5. A. Benassi, S. Cohen, J. Istas and S. Jaffard, Identification of filtered white noises. Stochastic Process. Appl. 75 (1998) 31–49. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Benassi, S. Jaffard and D. Roux, Elliptic Gaussian random processes. Rev. Mathem. Iberoamericana. 13 (1997) 19–89. [Google Scholar]
  7. H. Biermé, Champs aléatoires : autosimilarité, anisotropie et étude directionnelle. PhD thesis, Université d'Orléans, (2005). [Google Scholar]
  8. A. Bonami and A. Estrade, Anisotropic analysis of some Gaussian models. J. Fourier Anal. Appl. 9 (2003) 215–236. [CrossRef] [MathSciNet] [Google Scholar]
  9. G. Chan, An effective method for simulating Gaussian random fields, in Proceedings of the statistical Computing section, 133–138, (1999). Amerir. Statist. [Google Scholar]
  10. J.F. Coeurjolly, Inférence statistique pour les mouvements browniens fractionnaires et multifractionnaires. PhD thesis, Université Joseph Fourier (2000). [Google Scholar]
  11. J.F. Coeurjolly, Estimating the parameters of fractional Brownian motion by discrete variations of its sample paths. Stat. Inference Stoch. Process. 4 (2001) 199–227. [CrossRef] [MathSciNet] [Google Scholar]
  12. D. Dacunha-Castelle and M. Duflo, Probabilités et statistiques, Vol. 2. Masson (1983). [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. N. Enriquez, A simple construction of the fractional brownian motion. Stochastic Process. Appl. 109 (2004) 203–223. [CrossRef] [MathSciNet] [Google Scholar]
  15. J. Istas and G. Lang, Quadratic variations and estimation of the local Hölder index of a Gaussian process. Ann. Inst. Henri Poincaré, Prob. Stat. 33 (1997) 407–436. [Google Scholar]
  16. R. Jennane, R. Harba, E. Perrin, A. Bonami and A. Estrade, Analyse de champs browniens fractionnaires anisotropes. 18e colloque du GRETSI (2001) 99–102. [Google Scholar]
  17. L.M. Kaplan and C.C.J. Kuo, An Improved Method for 2-d Self-Similar Image Synthesis. IEEE Trans. Image Process. 5 (1996) 754–761. [CrossRef] [PubMed] [Google Scholar]
  18. J.T. Kent and A.T.A. Wood, Estimating the fractal dimension of a locally self-similar Gaussian process by using increments. J. Roy. Statist. Soc. Ser. B 59 (1997) 679–699. [MathSciNet] [Google Scholar]
  19. G. Lang and F. Roueff, Semi-parametric estimation of the Hölder exponent of a stationary Gaussian process with minimax rates. Stat. Inference Stoch. Process. 4 (2001) 283–306. [CrossRef] [MathSciNet] [Google Scholar]
  20. S. Leger, Analyse stochastique de signaux multi-fractaux et estimations de paramètres. Ph.D. thesis, Université d'Orléans, (2000). [Google Scholar]
  21. B.B. Mandelbrot and J. Van Ness, Fractional Brownian motion, fractionnal noises and applications. Siam Review 10 (1968) 422–437. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  22. Y. Meyer, F. Sellan and M.S. Taqqu, Wavelets, Generalised White Noise and Fractional Integration: The Synthesis of Fractional Brownian Motion. J. Fourier Anal. Appl. 5 (1999) 465–494. [CrossRef] [MathSciNet] [Google Scholar]
  23. I. Norros and P. Mannersalo, Simulation of Fractional Brownian Motion with Conditionalized Random Midpoint Displacement. Technical report, Advances in Performance analysis, (1999). [Google Scholar]
  24. R.F. Peltier and J. Lévy Véhel, Multifractional Brownian motion: definition and preliminary results. Technical report, INRIA, (1996). [Google Scholar]
  25. E. Perrin, R. Harba, C. Berzin-Joseph, I. Iribarren and A. Bonami, nth-order fractional Brownian motion and fractional Gaussian noises. IEEE Trans. Sign. Proc. 45 (2001) 1049–1059. [CrossRef] [Google Scholar]
  26. E. Perrin, R. Harba, R. Jennane and I. Iribarren, Fast and Exact Synthesis for 1-D Fractional Brownian Motion and Fractional Gaussian Noises. IEEE Signal Processing Letters 9 (2002) 382–384. [CrossRef] [Google Scholar]
  27. V. Pipiras, Wavelet-based simulation of fractional Brownian motion revisited. Preprint, (2004). [Google Scholar]
  28. A.G. Ramm and A.I. Katsevich, The Radon Transform and Local Tomography. CRC Press (1996). [Google Scholar]
  29. M.L. Stein, Fast and exact simulation of fractional Brownian surfaces. J. Comput. Graph. Statist. 11 (2002) 587–599. [CrossRef] [MathSciNet] [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.