Singularity functions for fractional processes : application to the fractional brownian sheet
Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 2, p. 187-205
@article{AIHPB_2006__42_2_187_0,
     author = {Cohen, Serge and Guyon, Xavier and Perrin, Olivier and Pontier, Monique},
     title = {Singularity functions for fractional processes : application to the fractional brownian sheet},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {42},
     number = {2},
     year = {2006},
     pages = {187-205},
     doi = {10.1016/j.anihpb.2005.03.002},
     zbl = {1095.60011},
     mrnumber = {2199797},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2006__42_2_187_0}
}
Cohen, Serge; Guyon, Xavier; Perrin, Olivier; Pontier, Monique. Singularity functions for fractional processes : application to the fractional brownian sheet. Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 2, pp. 187-205. doi : 10.1016/j.anihpb.2005.03.002. http://www.numdam.org/item/AIHPB_2006__42_2_187_0/

[1] A. Ayache, S. Léger, M. Pontier, Drap brownien fractionnaire, Potential Anal. 17 (1) (2002) 31-43. | MR 1906407 | Zbl 1006.60029

[2] G. Baxter, A strong limit theorem for Gaussian processes, Proc. Amer. Soc. 7 (1956) 522-527. | MR 90920 | Zbl 0070.36304

[3] A. Benassi, S. Cohen, J. Istas, S. Jaffard, Identification of filtered white noises, Stochastic Process. Appl. 75 (1998) 31-49. | MR 1629014 | Zbl 0932.60037

[4] J.-F. Coeurjolly, J. Istas, Cramér-Rao bounds for fractional Brownian motions, Statist. Probab. Lett. (2001). | MR 1856169 | Zbl 1092.62574

[5] S. Cohen, X. Guyon, O. Perrin, M. Pontier, Identification of an isometric transformation of the standard Brownian sheet, à paraître au J. Statist. Plann. Inference, 2004. | MR 2253765 | Zbl 1089.60047

[6] R. Dahlhaus, Efficient parameter estimation for self-similar processes, Ann. Statist. 17 (1989) 1749-1766. | MR 1026311 | Zbl 0703.62091

[7] D. Feyel, A. De La Pradelle, On fractional Brownian processes, Potential Anal. 10 (3) (1999) 273-288. | MR 1696137 | Zbl 0944.60045

[8] E.G. Gladyshev, A new limit theorem for Gaussian process, Theory Probab. Appl. 6 (1961) 52-61. | MR 145574 | Zbl 0107.12601

[9] X. Guyon, J. Léon, Convergence en loi des H-variations d'un processus gaussien stationnaire, Ann. Inst. H. Poincaré 25 (1989) 265-282. | Numdam | MR 1023952 | Zbl 0691.60017

[10] J. Istas, G. Lang, Quadratic variations and estimation of the Hölder index of a Gaussian process, Ann. Inst. H. Poincaré 33 (4) (1997) 407-436. | Numdam | MR 1465796 | Zbl 0882.60032

[11] A. Kamont, On the fractional anisotropic Wiener field, Probab. Math. Statist. 18 (1996) 85-98. | MR 1407935 | Zbl 0857.60046

[12] R. Klein, E. Giné, On quadratic variations of processes with Gaussian increments, Ann. Probab. 3 (4) (1975) 716-721. | MR 378070 | Zbl 0318.60031

[13] S. Léger, Analyse stochastique de signaux multi-fractaux et estimations de paramètres, PhD thesis, Université d'Orléans, 2000.

[14] O. Perrin, Quadratic variation for Gaussian processes and application to time deformation, Stochastic Process. Appl. 82 (2) (1999) 293-305. | MR 1700011 | Zbl 0997.60038