Some comparisons for Gaussian processes

Vitale, Richard

doi:10.1090/S0002-9939-00-05367-3

Some comparisons for Gaussian processes
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Proc. Amer. Math. Soc. 128 (2000), 3043-3046 Request permission

Abstract:

Extensions and variants are given for the well-known comparison principle for Gaussian processes based on ordering by pairwise distance.

References

Robert J. Adler, An introduction to continuity, extrema, and related topics for general Gaussian processes, Institute of Mathematical Statistics Lecture Notes—Monograph Series, vol. 12, Institute of Mathematical Statistics, Hayward, CA, 1990. MR 1088478
Ralph Alexander, Lipschitzian mappings and total mean curvature of polyhedral surfaces. I, Trans. Amer. Math. Soc. 288 (1985), no. 2, 661–678. MR 776397, DOI 10.1090/S0002-9947-1985-0776397-6
X. Fernique, Regularité des trajectoires des fonctions aléatoires gaussiennes, École d’Été de Probabilités de Saint-Flour, IV-1974, Lecture Notes in Math., Vol. 480, Springer, Berlin, 1975, pp. 1–96 (French). MR 0413238
Fernique, X. (1997). Fonctions aléatoires gaussiennes vecteurs aléatoires gaussiens. CRM, Montreal.
Yehoram Gordon, Some inequalities for Gaussian processes and applications, Israel J. Math. 50 (1985), no. 4, 265–289. MR 800188, DOI 10.1007/BF02759761
Yehoram Gordon, Elliptically contoured distributions, Probab. Theory Related Fields 76 (1987), no. 4, 429–438. MR 917672, DOI 10.1007/BF00960067
Yehoram Gordon, Majorization of Gaussian processes and geometric applications, Probab. Theory Related Fields 91 (1992), no. 2, 251–267. MR 1147616, DOI 10.1007/BF01291425
Jean-Pierre Kahane, Une inégalité du type de Slepian et Gordon sur les processus gaussiens, Israel J. Math. 55 (1986), no. 1, 109–110 (French, with English summary). MR 858463, DOI 10.1007/BF02772698
Ledoux, M. and Talagrand, M. (1985). Probability in Banach Spaces. Springer, New York.
M. A. Lifshits, Gaussian random functions, Mathematics and its Applications, vol. 322, Kluwer Academic Publishers, Dordrecht, 1995. MR 1472736, DOI 10.1007/978-94-015-8474-6
M. B. Marcus and L. A. Shepp, Sample behavior of Gaussian processes, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971) Univ. California Press, Berkeley, Calif., 1972, pp. 423–441. MR 0402896
Schläfli, L. (1858). On the multiple integral whose limits are $p_1=a_1x+b_1y+\cdots +h_1z>0,\cdots ,p_n>0, x^2+y^2+\cdots +z^2<1$. Quart. J. Math. Pure Appl. 2, 261–301, also, (1860) 3, 54–68.
David Slepian, The one-sided barrier problem for Gaussian noise, Bell System Tech. J. 41 (1962), 463–501. MR 133183, DOI 10.1002/j.1538-7305.1962.tb02419.x
V. N. Sudakov, Gaussian random processes, and measures of solid angles in Hilbert space, Dokl. Akad. Nauk SSSR 197 (1971), 43–45 (Russian). MR 0288832
V. N. Sudakov, Geometric problems in the theory of infinite-dimensional probability distributions, Proc. Steklov Inst. Math. 2 (1979), i–v, 1–178. Cover to cover translation of Trudy Mat. Inst. Steklov 141 (1976). MR 530375
Richard A. Vitale, Covariance identities for normal variables via convex polytopes, Statist. Probab. Lett. 30 (1996), no. 4, 363–368. MR 1422588, DOI 10.1016/S0167-7152(96)00003-X