Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes
Tóm tắt
Từ khóa
Tài liệu tham khảo
Istas, J. and Lang, G. (1997). Quadratic variations and estimation of the local Hölder index of a Gaussian process. <i>Ann. Inst. H. Poincaré Probab. Statist.</i> <b>33</b> 407–436.
Isserlis, L. (1918). On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables. <i>Biometrika</i> <b>12</b> 134–139.
Adler, R.J. (1981). <i>The Geometry of Random Fields</i>. Chichester: Wiley.
Ayache, A., Bonami, A. and Estrade, A. (2005). Identification and series decomposition of anisotropic Gaussian fields. In <i>Proceedings of 5th ISAAC Congrees</i>. Catania.
Baxter, G. (1956). A strong limit theorem for Gaussian processes. <i>Proc. Amer. Soc.</i> <b>7</b> 522–527.
Benassi, A., Jaffard, S. and Roux, D. (1997). Elliptic Gaussian random processes. <i>Rev. Math. Iboamerica</i> <b>13</b> 7–18.
Bégyn, A. (2005). Quadratic variations along irregular subdivisions for Gaussian processes. <i>Electronic J. Probab.</i> <b>10</b> 691–717.
Biermé, H. (2006). Estimation of anisotropic Gaussian fields through Radon transform. Submitted article. Available at http://www.univ-orleans.fr/mapmo/membres/bierme/recherche/Estimation.pdf.
Bingham, H., Goldie, C. and Teugels, J. (1989). <i>Regular Variation</i>. Cambridge: Cambridge Univ. Press.
Bonami, A. and Estrade, A. (2003). Anisotropic analysis of some Gaussian models. <i>J. Fourier Anal. Appl.</i> <b>9</b> 215–236.
Coeurjolly, J. (2000). Inférence statistique pour les mouvements Brownien fractionnaires et multifractionnaires (French). Ph.D. thesis, Univ. Grenoble I.
Cohen, S., Guyon, X., Perrin, O. and Pontier, M. (2005). Singularity functions for fractional processes, and application to fractional Brownian sheet. <i>Ann. Inst. H. Poincaré Probab. Statist.</i> <b>42</b> 187–205.
Dieudonné, J. (1980). <i>Calcul Infinitésimal (French)</i>. Paris: Hermann.
Hanson, D. and Wright, F. (1971). A bound on tail probabilities for quadratic forms in indenpedent random variables. <i>Ann. Math. Statist.</i> <b>42</b> 1079–1083.
Houdré, C. and Villa, J. (2003). An example of infinite dimensional quasi-helix. <i>Contemp. Math.</i> <b>336</b> 195–201. Providence, RI: Amer. Math. Soc.
Samorodnitsky, G. and Taqqu, M. (1994). <i>Stable Non-Gaussian Random Processes</i>. London: Chapmann and Hall.
Wong, R. (1989). <i>Asymptotic Approximation of Integrals</i>. Boston: Academic Press.