Quadratic variations along irregular subdivisions for gaussian processes

Electronic Journal of Probability

Volumn 10, Issue , 2005, Pages 691-717

  Begyn, Arnaud ^a  

^a UNIVERSITÉ PAUL SABATIER   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23244442846     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v10-245     Document Type: Article

References (17)

1. A. Adler. The geometry of random fields. Ed. John Wiley and Sons, 1981.
2. G. Baxter. A strong limit theorem for Gaussian processes. Proc. Amer. Soc., 7:522-527, 1956.
3. A. Benassi, S. Cohen, J. Istas, and S. Jaffard. Identification of filtered white noises. Stoch. Prob. Appl., 75:31-49, 1998.
4. A. Benassi, S. Jaffard, and D. Roux. Elliptic Gaussian random processes. Rev. Math. Iboamerica, 13:7-18, 1997.
5. d. Journ. Of Comput. And Graph. Statistics., 3:409-432, 1994.
6. P. Cheredito, H. Kawaguchi, and M. Maejima. Fractional Ornstein-Uhlenbeck processes. Elect. Journ. Of Proba., 8(3):1-14, 2003.
7. J.F. Coeurjolly. Inference statistique pour les mouvements Brownien fractionnaires et multifractionnaires. (French). PhD thesis, Üniversite Joseph Fourier Grenoble I., 2000.
8. J.F. Coeurjolly. Estimating the parameters of a fractional Brownian motion by discrete variations of its sample paths. Stat. Inference Stoch. Process., 4(2):199-227, 2001.
9. S. Cohen, X. Guyon, O. Perrin, and M. Pontier. Singularity functions for fractional processes, and application to fractional Brownian sheet. To appear in Annales de l’I.H.P.
10. R.M. Dudley. Sample functions of the Gaussian process. Ann. Probability, 1:66-103, 1973.
11. E.G. Gladyshev. A new limit theorem for stochastic processes with Gaussian increments. Theor. Prob. Appl., 6(1):52-61, 1961.
12. X. Guyon and J. León. Convergence in law of the H-variations of a stationary Gaussian process in R. Ann. Inst. H. Poincare Probab. Statist., 25(3):265-282, 1989.
13. D.L. Hanson and F.T. Wright. A bound on tail probabilities for quadratic forms in indepedent random variables. Ann. Math. Statist., 42:1079-1083, 1971.
14. J. Istas and G. Lang. Quadratic variations and estimation of the local Holder index of a Gaussian process. Annales de l’I.H.P., 33:407-436, 1997.
15. R. Klein and E. Gine. On quadratic variations of processes with Gaussian increments. Annals of Probability., 3(4):716-721, 1975.
16. J.W. Lamperti. Semi-stable stochastic processes. Trans. Amer. Math. Soc., 104:62-78, 1962.
17. P. Levy. Le mouvement Brownien plan. (french). Amer. J. Math., 62:487-550, 1940.