Some Probability and Entropy Estimates for Gaussian Measures

作者: V. Goodman

DOI: 10.1007/978-1-4684-6781-9_8

关键词:

摘要: We compare two estimates for the measure of Banach neighborhoods Hilbert balls in reproducing kernel space. Borell’s estimate [1] is quite general and known to be sharp certain cases which involve small probabilities. However, Talagrand [7] Goodman [4] use openness sets obtain alternative probability near one.

参考文章(6)
Christer Borell, The Brunn-Minkowski inequality in Gauss space Inventiones Mathematicae. ,vol. 30, pp. 207- 216 ,(1975) , 10.1007/BF01425510
J. Hoffmann-Jørgensen, L. A. Shepp, R. M. Dudley, On the Lower Tail of Gaussian Seminorms Annals of Probability. ,vol. 7, pp. 319- 342 ,(1979) , 10.1007/978-1-4419-5821-1_14
Victor Goodman, Characteristics of Normal Samples Annals of Probability. ,vol. 16, pp. 1281- 1290 ,(1988) , 10.1214/AOP/1176991690
V. Goodman, J. Kuelbs, J. Zinn, Some Results on the LIL in Banach Space with Applications to Weighted Empirical Processes Annals of Probability. ,vol. 9, pp. 713- 752 ,(1981) , 10.1214/AOP/1176994305
R. M. Dudley, The Sizes of Compact Subsets of Hilbert Space and Continuity of Gaussian Processes Journal of Functional Analysis. ,vol. 1, pp. 125- 165 ,(1967) , 10.1007/978-1-4419-5821-1_11
Michel Talagrand, Sur l'intégrabilité des vecteurs gaussiens Probability Theory and Related Fields. ,vol. 68, pp. 1- 8 ,(1984) , 10.1007/BF00535169