Free Access
Volume 17, 2013
Page(s) 307 - 327
Published online 17 May 2013
  1. P. Abry, P. Flandrin, M.S. Taqqu and D. Veitch, Self-similarity and long-range dependence through the wavelet lens, in Theory and applications of long-range dependenc. Birkhauser, Boston (2003). [Google Scholar]
  2. M.A. Arcones, Limit theorems for nonlinear functionals of a stationary Gaussian sequence of vectors. Ann. Probab. 22 (1994) 2242–2274. [CrossRef] [Google Scholar]
  3. A. Ayache and M.S. Taqqu, Rate optimality of wavelet series approximations of fractional Brownian motions. J. Fourier Anal. Appl. 9 (2003) 451–471. [CrossRef] [MathSciNet] [Google Scholar]
  4. A. Ayache and M.S. Taqqu, Multifractional process with random exponent. Publ. Math. 49 (2005) 459–486. [CrossRef] [Google Scholar]
  5. A. Ayache, P. Bertrand and J. Lévy-Véhel, A central limit theorem for the generalized quadratic variation of the step fractional Brownian motion. Stat. Inference Stoch. Process. 10 (2007) 1–27. [CrossRef] [MathSciNet] [Google Scholar]
  6. J.M. Bardet and P.R. Bertrand, Definition, properties and wavelet analysis of multiscale fractional Brownian motions. Fractals 15 (2007) 73–87. [CrossRef] [Google Scholar]
  7. J.M. Bardet and P.R. Bertrand, Identification of the multiscale fractional Brownian motion with biomechanical applications. J. Time Ser. Anal. 28 (2007) 1–52. [CrossRef] [MathSciNet] [Google Scholar]
  8. J.M. Bardet and P.R. Bertrand, A nonparametric estimator of the spectral density of a continuous-time Gaussian process observed at random times. Scand. J. Stat. 37 (2010) 458–476. [CrossRef] [MathSciNet] [Google Scholar]
  9. J.M. Bardet and D. Surgailis, Nonparametric estimation of the local hurst function of multifractional Gaussian processes, Stoch. Proc. Appl. 123 (2013) 1004–1045. [Google Scholar]
  10. J.M. Bardet and D. Surgailis, Measuring roughness of random paths by increment ratios. Bernoulli 17 (2011) 749–780. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. Bégyn, Functional limit theorems for generalized quadratic variations of Gaussian processes. Stoch. Proc. Appl. 117 (2007) 1848–1869. [CrossRef] [Google Scholar]
  12. A. Benassi, S. Jaffard and D. Roux, Gaussian processes and pseudodifferential elliptic operators. Rev. Mat. Iberoam. 13 (1997) 19–81. [Google Scholar]
  13. A. Benassi, S. Cohen and J. Istas, Identifying the multifractional function of a Gaussian process. Stat. Probab. Lett. 39 (1998) 337–345. [Google Scholar]
  14. P.R. Bertrand, A. Hamdouni and S. Khadhraoui, Modelling NASDAQ series by sparse multifractional Brownian motion. Method. Comput. Appl. Probab. 14 (2012) 107–124. [CrossRef] [Google Scholar]
  15. H. Biermé, A. Bonami and J. Leon, Central limit theorems and quadratic variations in terms of spectral density. Electronic Journal of Probability 16 (2011) 362–395. [MathSciNet] [Google Scholar]
  16. Pa. Billingsley, Probability and measure, 2nd edition. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons Inc., New York (1986). [Google Scholar]
  17. K. Bružaitė and M. Vaičiulis, The increment ratio statistic under deterministic trends. Lith. Math. J. 48 (2008) 256–269. [CrossRef] [MathSciNet] [Google Scholar]
  18. G. Chan and A.T.A. Wood, Simulation of multifractal Brownian motions, Proc. of Computational Statistics (1998) 233–238. [Google Scholar]
  19. P. Cheridito, Arbitrage in fractional Brownian motion models. Finance Stoch. 7 (2003) 533–553. [CrossRef] [MathSciNet] [Google Scholar]
  20. J.F. Coeurjolly, Estimating the parameters of a fractional Brownian motion by discrete variations of its sample paths. Stat. Inference Stoch. Process. 4 (2001) 199–227. [CrossRef] [MathSciNet] [Google Scholar]
  21. J.-F. Coeurjolly, Identification of multifractional Brownian motions. Bernoulli 11 (2005) 987–1008. [CrossRef] [MathSciNet] [Google Scholar]
  22. S. Cohen, From self-similarity to local self-similarity: the estimation problem, Fractal: Theory and Applications in Engineering, edited by M. Dekking, J. Lévy Véhel, E. Lutton and C. Tricot. Springer Verlag (1999). [Google Scholar]
  23. H. Cramèr and M.R. Leadbetter, Stationary and Related Stochastic Processes. Sample Function Properties and Their Applications, Wiley and Sons, London (1967). [Google Scholar]
  24. M. Fhima, Ph.D. thesis (2011) in preparation. [Google Scholar]
  25. X. Guyon and J. Leon, Convergence en loi des h-variations d’un processus Gaussien stationnaire. Ann. Inst. Henri Poincaré 25 (1989) 265–282. [Google Scholar]
  26. J. Istas and G. Lang, Quadratic variations and estimation of the hölder index of a Gaussian process. Ann. Inst. Henri Poincaré 33 (1997) 407–436. [Google Scholar]
  27. A.N. Kolmogorov, Wienersche spiralen und einige andere interessante kurven im hilbertschen raum. C.R. (Doklady) Acad. URSS (N.S.) 26 (1940) 115–118. [Google Scholar]
  28. J. Lévy-Véhel and R.F. Peltier, Multifractional Brownian motion: definition and preliminary results. Techn. Report RR-2645, INRIA (1996). [Google Scholar]
  29. B. Mandelbrot and J. Van Ness, Fractional Brownian motions, fractional noises and applications. SIAM Review 10 (1968) 422–437. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  30. Y. Meyer, F. Sellan and M.S. Taqqu, Wavelets, generalized white noise and fractional integration: the synthesis of fractional Brownian motions. J. Fourier Anal. Appl. 5 (1999) 465–494. [CrossRef] [MathSciNet] [Google Scholar]
  31. I. Nourdin and G. Peccati, Stein’s method on wiener chaos. Probab. Theory Relat. Fields 145 (2009) 75–118. [Google Scholar]
  32. I. Nourdin, G. Peccati and M. Podolskij, Quantitative Breuer-Major theorems, HAL: hal-00484096, version 2 (2010). [Google Scholar]
  33. G. Peccati and C.A. Tudor, Gaussian limits for vector-valued multiple stochastic integrals. Séminaire de Probabilités XXXVIII, Lecture Notes Math. 1857 (2005) 247–262. [Google Scholar]
  34. G. Samorodnitsky and M.S. Taqqu, Stable non-Gaussian random processes. Chapman & Hall (1994). [Google Scholar]
  35. A.S. Stoev and M.S. Taqqu, How rich is the class of multifractional brownian motions. Stoch. Proc. Appl. 116 (2006) 200–221. [Google Scholar]
  36. M. Stoncelis and M. Vaičiulis, Numerical approximation of some infinite Gaussian series and integrals. Nonlinear Anal.: Modelling and Control 13 (2008) 397–415. [Google Scholar]
  37. D. Surgailis, G. Teyssière and M. Vaičiulis, The increment ratio statistic. J. Multivar. Anal. 99 (2008) 510–541. [CrossRef] [Google Scholar]
  38. A.M. Yaglom, Some classes of random fields in n-dimensional space, related to stationary random processes. Theory Probab. Appl. 2 (1957) 273–320. [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.