Download this PDF file Fullscreen Fullscreen Off
References
- Anderson, T.W. (1955). The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. {it Proc. Amer. Math. Soc.} {bf 6}, 170--176. Math Review link
- Asmar, N.~H., Montgomery-Smith, S.J. (1994). On the distribution of Sidon series. {it Ark. Mat.} {bf 31}, 13--26. Math Review link
- Beckner, W. (1975). Inequalities in Fourier Analysis. {it Ann. of Math.} {bf 102}, 159--182. Math Review link
- Bingham, N.~H., Goldie, C.~M. and Teugels, J.~L. (1987). Regular variation. {it Cambridge University Press,} 491 pp. Math Review link
- Bonami, A. (1970). Etude des coefficients de Fourier des fonctiones de $L_p(G)$. {it Ann. de l'Institut Fourier} {bf 20}, 335--402. Math Review link
- Borell, C. (1979). On the integrability of Banach space valued Walsh polynomials. $;;$ {it S'eminaire de Probabilit'e XIII, Lecture in Math.} {bf 721}, 1--3. Math Review link
- Borell, C. (1984). On polynomial chaos and itegrability. {it Probability and Mathematical Statistics} {bf 3}, 191--203. Math Review link
- de~la~Pe~na, V., Montgomery-Smith, S.J. and Szulga, J. (1994). Contraction and decoupling inequalities for multilinear forms and U-statistics. {it Ann. of Prob.} {bf 22}, 1745--1765. Math Review link
- Gordon, Y. (1987). Elliptically contoured distributions. {it Prob. Theory Rel. Fields} {bf 76}, 429--438. Math Review link
- Gross, L. (1975). Logarithmic Sobolev inequalities. {it Amer. J. Math} {bf 97}, 1061--1083. Math Review link
- Khatri, C.G. (1967). On certain inequalities for normal distributions and their applications to simultaneous confidence bounds. {it Ann. Math. Statist.} {bf 38}, 1853--1867. Math Review link
- Krakowiak, W. and Szulga, J. (1988). Hypercontraction principle and random multilinear forms. {it Probability Theory and Related Fields} {bf 77}, 325--342. Math Review link
- Kuelbs, J., Li, W.V. and Shao, Q. (1995). Small ball estimates for fractional Brownian motion under H"older norm and Chung's functional LIL. {it J. Theor. Prob.} {bf 8}, 361-386. Math Review link
- Ledoux, M. and Talagrand, M. (1991). {it Probability on Banach Spaces}, Springer, Berlin. Math Review link
- Lewandowski, M., Ryznar, M. and .Zak, T. (1992). Stable measure of a small ball, {it Proc. Amer. Math. Soc.}, {bf 115}, 489--494. Math Review link
- Li, W.V. and Shao, Q. (1996). A note on the existence of the small ball constant for sup-norm for fractional Brownian motions assuming the correlation conjecture. Preprint.
- Marcus, M.~B. and Shepp, L. (1972). Sample behavior of Gaussian processes. {it Proc. of the Sixth Berkeley Symposium on Math. Statist. and Prob.} {bf vol. 2}, 423--421. Math Review link
- Nelson, E. (1966). A quartic interaction in two dimensions, in {it Mathematical Theory of Elementary Particles}, M.I.T. Press, 69--73. Math Review link
- Pitt, L.D. (1977). A Gaussian correlation inequality for symmetric convex sets. {it Ann. of Prob.} {bf 5}, 470--474. Math Review link
- Rychlik, E. (1993). Some necessary and sufficient conditions of $(p,q)$ hypercontractivity. Preprint.
- Schechtman, G., Schlumprecht, T. and Zinn, J. (1995). On the Gaussian measure of the intersection of symmetric, convex sets. Preprint.
- Sv id' ak, Z. (1967) Rectangular confidence regions for the means of multivariate normal distributions. {it J. Amer. Statist. Assoc.} {bf 62}, 626--633. Math Review link
- Sv id' ak, Z. (1968). On multivariate normal probabilities of rectangles: their dependence on correlations. {it Ann. Math. Statist.} {bf 39}, 1425--1434. Math Review link
- Slepian, D. (1962). The one-sided barrier problem for Gaussian noise. {it Bell System Tech. J. 41}, 463--501. Math Review not available.
- Szarek, S. (1991). Conditional numbers of random matrices. {it J. Complexity}, {bf 7}, 131--149. Math Review link
- Szarek, S. and Werner, E. (1995). Personal Communication.
- Szulga, J. (1990). A note on hypercontractivity of stable random variables. {it Ann. of Prob.} {bf 18}, 1746--1758. Math Review link
- Talagrand, M. (1994). The small ball problem for the Brownian sheet. {it Ann. of Probab.} {bf 22}, 1331--1354. Math Review link
- Tong, Y. L. (1980). {it Probability Inequalities in Multivariate Distributions}, Academic Press, New York. Math Review link

This work is licensed under a Creative Commons Attribution 3.0 License.