|
Some comparisons for Gaussian processes
Author(s):
Richard
A.
Vitale
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3043-3046.
MSC (1991):
Primary 60G15;
Secondary 60E15
Posted:
April 7, 2000
MathSciNet review:
1664383
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
Extensions and variants are given for the well-known comparison principle for Gaussian processes based on ordering by pairwise distance.
References:
-
- [1]
- Adler, R.J. (1990). An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes. Institute of Mathematical Statistics.MR 92g:60053
- [2]
- Alexander, R. (1985). Lipschitzian mappings and total mean curvature of polyhedral surfaces I. Trans. Amer. Math. Soc. 288, 661-678MR 86c:52004
- [3]
- Fernique, X. (1975). Regularité des trajectoires des fonctions aléatoires gaussiennes. Lecture Notes in Mathematics 480, 1-96, Springer.MR 54:1355
- [4]
- Fernique, X. (1997). Fonctions aléatoires gaussiennes vecteurs aléatoires gaussiens. CRM, Montreal. CMP 98:02
- [5]
- Gordon, Y. (1985). Some inequalities for Gaussian processes and applications. Israel J. Math. 50, 265-289. MR 87f:60058
- [6]
- Gordon, Y. (1987). Elliptically contoured distributions. Prob. Th. Rel. Fields 76, 429-438. MR 88m:60042
- [7]
- Gordon, Y. (1992). Majorization of Gaussian processes and geometric applications. Prob. Th. Rel. Fields 91, 251-267. MR 93a:60059
- [8]
- Kahane, J-P. (1986). Une inegalité du type de Slepian et Gordon sur les processus gaussiens. Israel J. Math. 55, 109-110.MR 88a:60075
- [9]
- Ledoux, M. and Talagrand, M. (1985). Probability in Banach Spaces. Springer, New York.
- [10]
- Lifshits, M.A. (1995). Gaussian Random Functions. Kluwer, Boston.MR 98k:60059
- [11]
- Marcus, M. and Shepp, L. (1972). Sample behavior of Gaussian processses. Proc. Sixth Berkeley Symp. Math. Stat. Prob. 2, 423-441.MR 53:6710
- [12]
- Schläfli, L. (1858). On the multiple integral whose limits are
. Quart. J. Math. Pure Appl. 2, 261-301, also, (1860) 3, 54-68. - [13]
- Slepian, D. (1962). The one-sided barrier problem for Gaussian processes. Bell System Tech. J. 41, 463-501. MR 24:A3017
- [14]
- Sudakov, V.N. (1971). Gaussian random processes and measures of solid angles in Hilbert space. Dokl. Akad. Nauk. SSR 197, 43-45.; English translation in Soviet Math. Dokl. (1971) 12, 412-415.MR 44:6027
- [15]
- Sudakov, V.N. (1976). Geometric Problems in the Theory of Infinite-Dimensional Probability Distributions. Trud. Mat. Inst. Steklov 141. English translation in Proc. Steklov Inst. Math 2, Amer. Math. Soc.MR 80e:60052
- [16]
- Vitale, R.A. (1996). Covariance identities for normal random variables via convex polytopes. Stat. Prob. Letters 30, 363-368.MR 98c:62103
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
60G15,
60E15
Retrieve articles in all Journals with
MSC (1991):
60G15,
60E15
Additional Information:
Richard
A.
Vitale
Affiliation:
Department of Statistics, U-120, University of Connecticut, Storrs, Connecticut 06269--3120
Email:
rvitale@uconnvm.uconn.edu
DOI:
10.1090/S0002-9939-00-05367-3
PII:
S 0002-9939(00)05367-3
Received by editor(s):
October 12, 1998
Received by editor(s) in revised form:
November 12, 1998
Posted:
April 7, 2000
Communicated by:
Stanley Sawyer
Copyright of article:
Copyright
2000,
American Mathematical Society
|