Quadratic variations and estimation of the local Hölder index of a gaussian process
Annales de l'I.H.P. Probabilités et statistiques (1997)
- Volume: 33, Issue: 4, page 407-436
 - ISSN: 0246-0203
 
Access Full Article
topHow to cite
topIstas, Jacques, and Lang, Gabriel. "Quadratic variations and estimation of the local Hölder index of a gaussian process." Annales de l'I.H.P. Probabilités et statistiques 33.4 (1997): 407-436. <http://eudml.org/doc/77576>.
@article{Istas1997,
	author = {Istas, Jacques, Lang, Gabriel},
	journal = {Annales de l'I.H.P. Probabilités et statistiques},
	keywords = {quadratic variation; estimation; local Hölder index; Gaussian process; asymptotic normality; central limit theorem},
	language = {eng},
	number = {4},
	pages = {407-436},
	publisher = {Gauthier-Villars},
	title = {Quadratic variations and estimation of the local Hölder index of a gaussian process},
	url = {http://eudml.org/doc/77576},
	volume = {33},
	year = {1997},
}
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
PB  - Gauthier-Villars
VL  - 33
IS  - 4
SP  - 407
EP  - 436
LA  - eng
KW  - quadratic variation; estimation; local Hölder index; Gaussian process; asymptotic normality; central limit theorem
UR  - http://eudml.org/doc/77576
ER  - 
References
top- 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. Zbl0747.60039MR1088478
 - R.J. Adler and R. Pyke, Uniform quadratic variation for Gaussian processes, Stoch. Proc. Appl., Vol. 48, 1993, pp. 191-209. Zbl0783.60040MR1244542
 - 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. Zbl0751.62036MR1113093
 - H. Cramer and M.R. Leadbetter, Stationary and related stochastic processes, Wiley, New York, 1967. Zbl0162.21102MR217860
 - M. Czörgo and P. Révész, Strong approximation in probability and statistics, Academic Press, 1981. MR666546
 - D. Dacunha-Castelle and M. Duflo, Probabilités et statistiques, Tome 2, Masson, 1983. Zbl0535.62004MR732786
 - I. Daubechies, Orthonormal bases of compactly supported wavelets, Commun. Pure Appl. Math., Vol. 41, Nov 1988, pp. 909-996. Zbl0644.42026MR951745
 - 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. Zbl0776.62033MR1211787
 - U. Grenander, Abstract inference, Wiley, 1981. Zbl0505.62069MR599175
 - X. Guyon, Variations des champs gaussiens stationnaires: applications à l'identification, Proba. Th. Rel. Fields, n° 75, 1987, pp. 179-193. Zbl0596.60051MR885461
 - 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. Zbl0691.60017MR1023952
 - P. Hall and A. Wood, On the performance of box-counting estimators of fractal dimension, Biometrika, , Vol. 80, 1993, pp. 246-252. Zbl0769.62062MR1225230
 - 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. Zbl0815.62060MR1312323
 - 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. Zbl0392.60037MR543837
 - J. Istas, Wavelet coefficients of a Gaussian process and applications, Ann. Inst. Henri Poincare, Vol. 28, n° 4, 1992, pp. 537-556. Zbl0760.60041MR1193084
 - 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. Zbl0768.62027MR1209273
 - 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. Zbl0727.60040MR1116798
 - L. Luenberger, Introduction to dynamical systems: theory and applications, Wiley, 1979. Zbl0458.93001
 - B. Mandelbrot and J. van NessFractional Brownian Motions, Fractional Noises and Applications. SIAM Review, 1968, 10, pp. 422-437. Zbl0179.47801MR242239
 - 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. Zbl0735.62083MR1139838
 
Citations in EuDML Documents
top- Jean-Marc Bardet, Les cours d'actifs financiers sont-ils autosimilaires ?
 - Serge Cohen, Xavier Guyon, Olivier Perrin, Monique Pontier, Singularity functions for fractional processes : application to the fractional brownian sheet
 - Hermine Biermé, Frédéric Richard, Estimation of anisotropic gaussian fields through Radon transform
 - Jacques Istas, Identification des paramètres d'un processus gaussien fractionnaire
 - Céline Lacaux, Real harmonizable multifractional Lévy motions
 - Hermine Biermé, Frédéric Richard, Estimation of anisotropic Gaussian fields through Radon transform
 - Pierre Raphaël Bertrand, Mehdi Fhima, Arnaud Guillin, Local estimation of the Hurst index of multifractional brownian motion by increment ratio statistic method
 - Ewaryst Rafajłowicz, Marek Wnuk, Wojciech Rafajłowicz, Local detection of defects from image sequences
 - Jacques Istas, Manifold indexed fractional fields
 - Jacques Istas, Manifold indexed fractional fields
 
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.