Quadratic variations and estimation of the local Hölder index of a gaussian process
Istas, Jacques ; Lang, Gabriel
Annales de l'I.H.P. Probabilités et statistiques, Tome 33 (1997), p. 407-436 / Harvested from Numdam
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@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},
     volume = {33},
     year = {1997},
     pages = {407-436},
     mrnumber = {1465796},
     zbl = {0882.60032},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 407-436. http://gdmltest.u-ga.fr/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 1088478 | Zbl 0747.60039

R.J. Adler and R. Pyke, Uniform quadratic variation for Gaussian processes, Stoch. Proc. Appl., Vol. 48, 1993, pp. 191-209. | MR 1244542 | Zbl 0783.60040

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 1113093 | Zbl 0751.62036

H. Cramer and M.R. Leadbetter, Stationary and related stochastic processes, Wiley, New York, 1967. | MR 217860 | Zbl 0162.21102

M. Czörgo and P. Révész, Strong approximation in probability and statistics, Academic Press, 1981. | MR 666546

D. Dacunha-Castelle and M. Duflo, Probabilités et statistiques, Tome 2, Masson, 1983. | MR 732786 | Zbl 0535.62004

I. Daubechies, Orthonormal bases of compactly supported wavelets, Commun. Pure Appl. Math., Vol. 41, Nov 1988, pp. 909-996. | MR 951745 | Zbl 0644.42026

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 1211787 | Zbl 0776.62033

U. Grenander, Abstract inference, Wiley, 1981. | MR 599175 | Zbl 0505.62069

X. Guyon, Variations des champs gaussiens stationnaires: applications à l'identification, Proba. Th. Rel. Fields, n° 75, 1987, pp. 179-193. | MR 885461 | Zbl 0596.60051

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 1023952 | Zbl 0691.60017

P. Hall and A. Wood, On the performance of box-counting estimators of fractal dimension, Biometrika, , Vol. 80, 1993, pp. 246-252. | MR 1225230 | Zbl 0769.62062

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 1312323 | Zbl 0815.62060

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 543837 | Zbl 0392.60037

J. Istas, Wavelet coefficients of a Gaussian process and applications, Ann. Inst. Henri Poincare, Vol. 28, n° 4, 1992, pp. 537-556. | Numdam | MR 1193084 | Zbl 0760.60041

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 1209273 | Zbl 0768.62027

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 1116798 | Zbl 0727.60040

L. Luenberger, Introduction to dynamical systems: theory and applications, Wiley, 1979. | Zbl 0458.93001

B. Mandelbrot and J. Van Ness Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review, 1968, 10, pp. 422-437. | MR 242239 | Zbl 0179.47801

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 1139838 | Zbl 0735.62083