On the identification of the pointwise Hölder exponent of the generalized multifractional Brownian motion

Stochastic Processes and their Applications

Volumn 111, Issue 1, 2004, Pages 119-156

  Ayache, Antoine ^a,b   Véhel, Jacques Lévy ^c  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b UNIVERSITÉ PAUL SABATIER   (France)

^c INRIA   (France)

Author keywords

Fractional Brownian motion; Gaussian process; Generalized multifractional Brownian motion; Identification; Pointwise H lder exponent

Indexed keywords

EID: 1642419174     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2003.11.002     Document Type: Article

References (34)

1. Ayache A. The generalized multifractional field: a nice tool for the study of the generalized multifractional Brownian motion J. Fourier Anal. Appl. 8 2002 581-601
2. Ayache A. Léger S. 2000 The multifractional Brownian sheet. Ann. Mat. Blaise Pascal, to appear.
3. Ayache A. Lévy Véhel J. Generalized multifractional Brownian motion: definition and preliminary results In: Dekking M. Lévy Véhel J. Lutton E. Tricot C. (Eds.), Fractals: Theory and Applications in Engineering 1999 17-32 Springer Berlin
4. Ayache A. Lévy Véhel J. The generalized multifractional Brownian motion Statist. Inference Stochastic Process. 3 2000 7-18
5. Ayache A. Taqqu M.S. 2003 Multifractional processes with random exponent. Preprint.
6. Ayache A. Benassi A. Cohen S. Lévy Véhel J. 2001 Regularity and identification of generalized multifractional Gaussian processes. Séminaire de Probabilités, Springer, Berlin, to appear.
7. Ayache A. Jaffard S. Taqqu M.S. 2003 Multifractional processes with a most general multifractal spectrum. Preprint.
8. Benassi A. Jaffard S. Roux D. Elliptic Gaussian random processes Rev. Mat. Iberoamericana 13 1 1997 19-89
9. Benassi A. Cohen S. Istas J. Identifying the multifractional function of a Gaussian process Statist. Probab. Lett. 39 1998 31-49
10. Benassi A. Cohen S. Istas J. Jaffard S. Identification of filtered white noises Stochastic Process. Appl. 75 1998 31-49
11. Benassi A. Bertrand P. Cohen S. Istas J. Identification of the Hurst exponent of a step multifractional Brownian motion Statist. Inference Stochastic Process. 3 2000 101-110
12. Beran J. Statistics for Long-Memory Processes 1994 Chapman & Hall London, UK
13. Coeurjolly J.F. 2000 Inférence statistique pour les Mouvements Brownien Fractionnaires et Multifractionnaires. Thèse de Doctorat, l'Université Joseph Fourier, Grenoble, France.
14. Daoudi K. Lévy Véhel J. Meyer Y. Construction of continuous functions with prescribed local regularity Const. Approx. 014 03 1998 349-385
15. Doukhan P. Oppenheim G. Taqqu M.S. (Eds.), 2002. Theory and Applications of Long-range Dependence. Birkhäuser, Boston.
16. Falconer K. Tangent fields and the local structure of random fields J. Theoret. Probab. 15 2002 731-750
17. Falconer K. The local structure of random processes J. London Math. Soc. 67 2003 657-672
18. Frisch U. Parisi G. In: Ghil M. Benzi R. Parisi G. (Eds.), Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics 1985 North-Holland Amsterdam
19. Guyon X. Leon G. Convergence en loi des h-variations d'un processus Gaussien stationnaire Ann. Inst. H Poincaré 25 1989 265-282
20. Herbin, E., From N parameter fractional Brownian motions to N parameter multifractional Brownian motions, Rocky Mountain J. Math., to appear.
21. Herbin E. Lévy Véhel J. 2003 2-microlocal analysis of Gaussian processes. Preprint.
22. Heyde C. Gay R. Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence Stochastic Process. Appl. 45 1993 169-182
23. Istas J. Lang G. Quadratic variations and estimation of the local Hölder index of a Gaussian process Ann. Inst. H Poincare 4 33 1997 407-436
24. Jacob N. Leopold H.G. Pseudo-differential operators with variable order of differentiation generating Feller semigroups Integral Equations Operator Theory 17 1993 544-553
25. Jaffard S. Functions with prescribed Hölder exponent Appl. Comput. Harm. Anal. 2 1995 400-401
26. Kikuchi A. Negoro A. On Markov processes generated by pseudo-differential operators of variable order Osaka J. Math. 34 1997 319-335
27. Kolmogorov A. Wienersche Spiralen und einige andere interessante Kurven in Hilbertsche Raum C.R. (Dokl.) Acad. Sci. USSR 26 1940 115-118
28. Komatsu T. On stable-like processes In: Watanabe S et al. (Eds.), Proceedings of the Seventh Japan-Russia Symposium on Probability Theory and Mathematic Statistics 1995 World Scientific Singapore
29. Mandelbrot B. Van Ness J. Fractional Brownian motion, fractional noises and applications SIAM Rev. 10 1968 422-437
30. Peitgen O. Saupe D. (Eds.), 1988. The Science of Fractal Images. Springer, New York.
31. Peltier R.F. Lévy Véhel J. 1995 Multifractional Brownian motion: definition and preliminary results. INRIA Res. Rept. 2645. Available at http://fractales.inria.fr
32. Robinson P. Gaussian semiparametric estimation of long-range dependence Ann. Statist. 23 1995 1630-1661
33. Samorodnitsky G. Taqqu M.S. Stable non-Gaussian random processes 1994 Chapman & Hall London
34. Taqqu M.S. Willinger W. Sherman R. Proof of a fundamental result in self-similar traffic modeling Comput. Commun. Rev. 27 2 1997 5-23