EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 18 (2014) ESAIM: PS, 18 (2014) 42-76 References
Free Access
Issue
ESAIM: PS
Volume 18, 2014
Page(s) 42 - 76
DOI https://doi.org/10.1051/ps/2012026
Published online 28 November 2013
  1. P. Abry and V. Pipiras, Wavelet-based synthesis of the Rosenblatt process. Eurasip Signal Processing 86 (2006) 2326–2339. [CrossRef] [Google Scholar]
  2. P. Abry and D. Veitch, Wavelet analysis of long–range-dependent traffic. IEEE Trans. Inform. Theory 44 (1998) 2–15. [CrossRef] [MathSciNet] [Google Scholar]
  3. P. Abry, D. Veitch and P. Flandrin, Long-range dependence: revisiting aggregation with wavelets. J. Time Ser. Anal. 19 (1998) 253–266. ISSN 0143-9782. [CrossRef] [Google Scholar]
  4. P. Abry, Helgason H. and V. Pipiras, Wavelet-based analysis of non-Gaussian long–range dependent processes and estimation of the Hurst parameter. Lithuanian Math. J. 51 (2011) 287–302. [CrossRef] [Google Scholar]
  5. J.-M. Bardet, Statistical study of the wavelet analysis of fractional Brownian motion. IEEE Trans. Inform. Theory 48 (2002) 991–999. [CrossRef] [MathSciNet] [Google Scholar]
  6. J.-M. Bardet and C.A. Tudor, A wavelet analysis of the Rosenblatt process: chaos expansion and estimation of the self-similarity parameter. Stochastic Process. Appl. 120 (2010) 2331–2362. [CrossRef] [MathSciNet] [Google Scholar]
  7. J.-M. Bardet, G. Lang, E. Moulines and P. Soulier, Wavelet estimator of long–range dependent processes. 19th “Rencontres Franco-Belges de Statisticiens” (Marseille, 1998). Stat. Inference Stoch. Process. 3 (2000) 85–99. [CrossRef] [MathSciNet] [Google Scholar]
  8. J.M. Bardet, H. Bibi and A. Jouini, Adaptive wavelet based estimator of the memory parameter for stationary gaussian processes. Bernoulli 14 (2008) 691–724. [CrossRef] [MathSciNet] [Google Scholar]
  9. J.-C. Breton and I. Nourdin, Error bounds on the non-normal approximation of hermite power variations of fractional brownian motion. Electron. Commun. Probab. 13 (2008) 482–493. [MathSciNet] [Google Scholar]
  10. A. Chronopoulou, C. Tudor and F. Viens, Self-similarity parameter estimation and reproduction property for non-gaussian Hermite processes. Commun. Stoch. Anal. 5 (2011) 161–185. [MathSciNet] [Google Scholar]
  11. M. Clausel, F. Roueff, M.S. Taqqu and C. Tudor, Large scale behavior of wavelet coefficients of non-linear subordinated processes with long memory. Appl. Comput. Harmonic Anal. 32 (2012) 223–241. [CrossRef] [Google Scholar]
  12. M. Clausel, F. Roueff, M.S. Taqqu and C. Tudor, High order chaotic limits of wavelet scalograms under long–range dependence. Technical report, Hal–Institut Telecom (2012). http://hal-institut-telecom.archives-ouvertes.fr/hal-00662317. [Google Scholar]
  13. R.L. Dobrushin and P. Major, Non-central limit theorems for nonlinear functionals of Gaussian fields. Z. Wahrsch. Verw. Gebiete 50 (1979) 27–52. [CrossRef] [MathSciNet] [Google Scholar]
  14. P. Embrechts and M. Maejima, Selfsimilar processes. Princeton University Press, Princeton, New York (2002). [Google Scholar]
  15. P. Flandrin, On the spectrum of fractional Brownian motions. IEEE Trans. Inform. Theory IT-35 (1989) 197–199. [CrossRef] [Google Scholar]
  16. P. Flandrin, Some aspects of nonstationary signal processing with emphasis on time-frequency and time-scale methods. Edited by J.M. Combes, A. Grossman and Ph. Tchamitchian, Wavelets. Springer-Verlag (1989) 68–98. [Google Scholar]
  17. P. Flandrin, Fractional Brownian motion and wavelets. Edited by M. Farge, J.C.R. Hung and J.C. Vassilicos, Fractals and Fourier Transforms-New Developments and New Applications. Oxford University Press (1991). [Google Scholar]
  18. P. Flandrin, Time-Frequency/Time-scale Analysis, 1st edition. Academic Press (1999). [Google Scholar]
  19. R. Fox and M.S. Taqqu. Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Statist. 14 (1986) 517–532. [CrossRef] [MathSciNet] [Google Scholar]
  20. L. Giraitis and D. Surgailis, Central limit theorems and other limit theorems for functionals of gaussian processes. Z. Wahrsch. verw. Gebiete 70 (1985) 191–212. [CrossRef] [MathSciNet] [Google Scholar]
  21. L. Giraitis and M.S. Taqqu, Whittle estimator for finite-variance non-gaussian time series with long memory. Ann. Statist. 27 (1999) 178–203. [CrossRef] [MathSciNet] [Google Scholar]
  22. A.J. Lawrance and N.T. Kottegoda, Stochastic modelling of riverflow time series. J. Roy. Statist. Soc. Ser. A 140 (1977) 1–47. [CrossRef] [Google Scholar]
  23. P. Major, Multiple Wiener-Itô integrals, vol. 849 of Lect. Notes Math. Springer, Berlin (1981). [Google Scholar]
  24. E. Moulines, F. Roueff and M.S. Taqqu, On the spectral density of the wavelet coefficients of long memory time series with application to the log-regression estimation of the memory parameter. J. Time Ser. Anal. 28 (2007) 155–187. [CrossRef] [Google Scholar]
  25. I. Nourdin and G. Peccati, Stein’s method meets Malliavin calculus: a short survey with new estimates. Technical report, Recent Advances in Stochastic Dynamics and Stochastic Analysis 8 (2010) 207–236. [CrossRef] [Google Scholar]
  26. I. Nourdin and G. Peccati, Stein’s method on wiener chaos. Probability Theory and Related Fields 154 (2009) 75–118. [CrossRef] [Google Scholar]
  27. D. Nualart, The Malliavin Calculus and Related Topics. Springer (2006). [Google Scholar]
  28. P.M. Robinson, Log-periodogram regression of time series with long range dependence. Ann. Statist. 23 (1995) 1048–1072. [CrossRef] [MathSciNet] [Google Scholar]
  29. P.M. Robinson, Gaussian semiparametric estimation of long range dependence. Ann. Statist. 23 (1995) 1630–1661. [CrossRef] [MathSciNet] [Google Scholar]
  30. F. Roueff and M. S. Taqqu, Central limit theorems for arrays of decimated linear processes. Stoch. Proc. Appl. 119 (2009) 3006–3041. [CrossRef] [Google Scholar]
  31. F. Roueff and M.S. Taqqu, Asymptotic normality of wavelet estimators of the memory parameter for linear processes. J. Time Ser. Anal. 30 (2009) 534–558. [CrossRef] [Google Scholar]
  32. A. Scherrer, Analyses statistiques des communications sur puce. Ph.D. thesis, École normale supérieure de Lyon (2006). Available on http://www.ens-lyon.fr/LIP/Pub/Rapports/PhD/PhD2006/PhD2006-09.pdf. [Google Scholar]
  33. M.S. Taqqu, A representation for self-similar processes. Stoch. Proc. Appl. 7 (1978) 55–64. [CrossRef] [Google Scholar]
  34. M.S. Taqqu, Central limit theorems and other limit theorems for functionals of gaussian processes. Z. Wahrsch. verw. Gebiete 70 (1979) 191–212. [Google Scholar]
  35. G.W. Wornell and A.V. Oppenheim, Estimation of fractal signals from noisy measurements using wavelets. IEEE Trans. Signal Process. 40 (1992) 611–623. [CrossRef] [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.