Quadratic variations and estimation of the local Hölder index of a gaussian process
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 4, pp. 407-436. 
@article{AIHPB_1997__33_4_407_0,
     author = {Istas, Jacques and Lang, Gabriel},
     title = {Quadratic variations and estimation of the local {H\"older} index of a gaussian process},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {407--436},
     publisher = {Gauthier-Villars},
     volume = {33},
     number = {4},
     year = {1997},
     mrnumber = {1465796},
     zbl = {0882.60032},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_1997__33_4_407_0/}
}
TY  - JOUR
AU  - Istas, Jacques
AU  - Lang, Gabriel
TI  - Quadratic variations and estimation of the local Hölder index of a gaussian process
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1997
SP  - 407
EP  - 436
VL  - 33
IS  - 4
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPB_1997__33_4_407_0/
LA  - en
ID  - AIHPB_1997__33_4_407_0
ER  - 
%0 Journal Article
%A Istas, Jacques
%A Lang, Gabriel
%T Quadratic variations and estimation of the local Hölder index of a gaussian process
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1997
%P 407-436
%V 33
%N 4
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPB_1997__33_4_407_0/
%G en
%F AIHPB_1997__33_4_407_0
Istas, Jacques; Lang, Gabriel. Quadratic variations and estimation of the local Hölder index of a gaussian process. Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997) no. 4, pp. 407-436. http://archive.numdam.org/item/AIHPB_1997__33_4_407_0/

R.J. Adler, An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes, I.M.S. Lecture Notes-Monograph Series, Vol. 12, 1990. | MR | Zbl

R.J. Adler and R. Pyke, Uniform quadratic variation for Gaussian processes, Stoch. Proc. Appl., Vol. 48, 1993, pp. 191-209. | MR | Zbl

J-M. Azaïs, Exact error evaluation in Gaussian process simulation, preprint, 1994.

P. Brugière, Estimation de la variance d'une diffusion, C. R. Acad. Sci., Tome 312, Série I, 1991, pp. 999-1004. | MR | Zbl

H. Cramer and M.R. Leadbetter, Stationary and related stochastic processes, Wiley, New York, 1967. | MR | Zbl

M. Czörgo and P. Révész, Strong approximation in probability and statistics, Academic Press, 1981. | MR

D. Dacunha-Castelle and M. Duflo, Probabilités et statistiques, Tome 2, Masson, 1983. | MR | Zbl

I. Daubechies, Orthonormal bases of compactly supported wavelets, Commun. Pure Appl. Math., Vol. 41, Nov 1988, pp. 909-996. | MR | Zbl

V. Genon-Catalot, C. Laredo and D. Picard, Non-parametric estimation of the diffusion coefficient by wavelets methods, Scand. J. of Statist., Vol. 19, 1992, p. 317-335. | MR | Zbl

U. Grenander, Abstract inference, Wiley, 1981. | MR | Zbl

X. Guyon, Variations des champs gaussiens stationnaires: applications à l'identification, Proba. Th. Rel. Fields, n° 75, 1987, pp. 179-193. | MR | Zbl

X. Guyon and J.R. Leon, Convergence en loi des H-variations d'un processus gaussien stationnaire, Ann. Inst. Henri Poincaré, Vol. 25, n° 3, 1989, pp. 265-282. | Numdam | MR | Zbl

P. Hall and A. Wood, On the performance of box-counting estimators of fractal dimension, Biometrika, , Vol. 80, 1993, pp. 246-252. | MR | Zbl

P. Hall, A. Wood and A. Feuerverger, Estimation of fractal index and fractal dimension of a Gaussian process by counting the number of level crossings, J. of Time Ser. Anal., n° 6, 15, 1994, pp. 587-606. | MR | Zbl

P. Hubert and J.-P. Carbonnel, Caractérisation fractale de la variabilité et de l'anisotropie des précipations intertropicales, C. R. Acad. Sci., Tome 307, Série II, 1988, pp. 909-914.

I.A. Ibragimov and Y.A. Rozanov, Gaussian random processes, Springer Verlag, 1978. | MR | Zbl

J. Istas, Wavelet coefficients of a Gaussian process and applications, Ann. Inst. Henri Poincare, Vol. 28, n° 4, 1992, pp. 537-556. | Numdam | MR | Zbl

J. Istas and C. Laredo, Estimation de la fonction de covariance d'un processus gaussien stationnaire par méthodes d'échelles, C. R. Acad. Sci., Tome 316, Série I, 1993, pp. 495-498. | MR | Zbl

G. Lang, Estimation de la régularité et de la longue dépendance de processus gaussiens. Thèse de l'université Toulouse III, 1994.

J.R. Leon and J. Ortega, Weak convergence of different types of variation for biparametric Gaussian processes, Colloquia Math. Soc. J. Bolyai, n° 57, 1989, Limit theorems in Proba. and Stat., Pecs Hungary. | MR | Zbl

L. Luenberger, Introduction to dynamical systems: theory and applications, Wiley, 1979. | Zbl

B. Mandelbrot and J. Van Ness Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review, 1968, 10, pp. 422-437. | MR | Zbl

A.P. Pentland, Fractal-based description of natural scenes, IEEE transactions on pattern analysis and machine intelligence, Vol. PAMI-6, n° 6, 1984, pp. 661-674.

P. Soulier, Déviation quadratique pour des estimateurs de la variance d'une diffusion, C. R. Acad. Sci., Tome 313, Série I, 1991, pp. 783-786. | MR | Zbl