Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A vectorial Slepian type inequality. Applications


Author: B. Khaoulani
Journal: Proc. Amer. Math. Soc. 118 (1993), 95-102
MSC: Primary 60G15; Secondary 46B07, 47N30
MathSciNet review: 1159173
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a new inequality for Gaussian processes; this inequality implies the Chevet's inequality and Gordon's inequalities. Some remarks on Gaussian proofs of Dvoretzky's theorem are given.


References [Enhancements On Off] (What's this?)

  • [C] Louis H. Y. Chen, An inequality for the multivariate normal distribution, J. Multivariate Anal. 12 (1982), no. 2, 306–315. MR 661566, 10.1016/0047-259X(82)90022-7
  • [Cv] S. Chevet, Séries de variables aléatoires Gaussiennes à valeurs dans $ E{\widehat \otimes _\varepsilon }F$. Application aux produits d'espaces de Wiener, Séminaire Maurey-Schwartz, exposé XiX 77/78.
  • [F] X. M. Fernique, Régularité des trajectoires des fonctions aléatoires Gaussiennes, Lecture Notes in Math., vol. 480, Springer-Verlag, New York, 1974.
  • [G1] Yehoram Gordon, Some inequalities for Gaussian processes and applications, Israel J. Math. 50 (1985), no. 4, 265–289. MR 800188, 10.1007/BF02759761
  • [G2] Yehoram Gordon, Elliptically contoured distributions, Probab. Theory Related Fields 76 (1987), no. 4, 429–438. MR 917672, 10.1007/BF00960067
  • [K] 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, 10.1007/BF02772698
  • [M] V. D. Milman, A new proof of A. Dvoretzky’s theorem on cross-sections of convex bodies, Funkcional. Anal. i Priložen. 5 (1971), no. 4, 28–37 (Russian). MR 0293374
  • [P] Gilles Pisier, Probabilistic methods in the geometry of Banach spaces, Probability and analysis (Varenna, 1985) Lecture Notes in Math., vol. 1206, Springer, Berlin, 1986, pp. 167–241. MR 864714, 10.1007/BFb0076302
  • [Sc] Gideon Schechtman, A remark concerning the dependence on 𝜀 in Dvoretzky’s theorem, Geometric aspects of functional analysis (1987–88), Lecture Notes in Math., vol. 1376, Springer, Berlin, 1989, pp. 274–277. MR 1008729, 10.1007/BFb0090061

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60G15, 46B07, 47N30

Retrieve articles in all journals with MSC: 60G15, 46B07, 47N30


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1159173-4
Article copyright: © Copyright 1993 American Mathematical Society