Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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 $p_1=a_1x+b_1y+\cdots+h_1z>0,\cdots,p_n>0, x^2+y^2+\cdots+z^2<1$. Quart. J. Math. Pure Appl. 2, 261-301, also, (1860) 3, 54-68.

[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




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia