On roughness indices for fractional fields

Bernoulli

Volumn 10, Issue 2, 2004, Pages 357-373

  Benassi, Albert ^a   Cohen, Serge ^b   Istas, Jacques ^c  

^a UNIVERSITÉ CLERMONT AUVERGNE   (France)

^b INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^c UNIV GRENOBLE ALPES   (France)

Author keywords

Identification; Local asymptotic self similarity; Second order fields; Stable fields

Indexed keywords

EID: 13344278798     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/bj/1082380223     Document Type: Article

References (15)

1. Abry, P., Delbeke, L. and Flandrin, P. (2000) Wavelet based estimator for the self-similarity parameter of α-stable processes. Preprint.
2. Benassi, A., Cohen, S. and Istas, J. (1998) Identifying the multifractional function of a Gaussian process. Statist. Probab. Lett., 39, 337-345.
3. Benassi, A., Cohen, S. and Istas, J. (2002) Identification and properties of real harmonizable fractional Lévy motions. Bernoulli, 8, 97-115.
4. Coeurjolly, J.-F. and Istas, J. (2001) Cramer-Rao bounds for fractional Brownian motions. Statist. Probab. Lett., 53, 435-447.
5. Cohen, S. and Istas, J. (2003) A universal estimator of local self-similarity. Submitted.
6. Dury, M.-E. (2001) Estimation du paramètre de Hurst de processus stables auto-similaires à accroissements stationnaires. C. R. Acad. Sci. Paris Sér. I, 333, 45-48.
7. Falconer, K. (2002) Tangent fields and the local structure of random fields, J. Theoret. Probab., 15, 731-750.
8. Falconer, K. (2003) The local structure of random processes. J. London Math. Soc. (2), 67, 657-672.
9. Istas, J. and Lang, G. (1997) Quadratic variations and estimation of the local Hölder index of a Gaussian process. Ann. Inst. H. Poincaré. Probab. Statist., 33(4), 407-436.
10. Janssen, A. (1982) Zero-one laws for infinitely divisible probability measures on groups. Z. Wahrscheinlichkeitstheorie Verw. Geb., 60, 119-138.
11. Kolmogorov, A. (1940) Wienersche Spiralen und einige andere interessante Kurven im Hilbertsche Raum, C. R. (Dokl.) Acad. Sci. URSS, 26, 115-118.
12. Mandelbrot, B. and Van Ness, J. (1968) Fractional Brownian motions, fractional noises and applications. SIAM Rev., 10, 422-437.
13. Neveu, J. (1968) Processus aléatoires gaussiens. Montreal: Presses de l'Université de Montréal.
14. Rosinski, J. (1989) On path properties of certain infinitely divisible processes. Stochastic Process. Appl. 33, 73-87.
15. Samorodnitsky, G. and Taqqu, M. (1994) Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. New York: Chapman & Hall.