Small ball probabilities for the Slepian Gaussian fields

Authors:
Fuchang Gao and Wenbo V. Li

Journal:
Trans. Amer. Math. Soc. **359** (2007), 1339-1350

MSC (2000):
Primary 60G15; Secondary 42A55

Published electronically:
October 16, 2006

MathSciNet review:
2262853

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The -dimensional Slepian Gaussian random field is a mean zero Gaussian process with covariance function for and . Small ball probabilities for are obtained under the -norm on , and under the sup-norm on which implies Talagrand's result for the Brownian sheet. The method of proof for the sup-norm case is purely probabilistic and analytic, and thus avoids ingenious combinatoric arguments of using decreasing mathematical induction. In particular, Riesz product techniques are new ingredients in our arguments.

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Additional Information

**Fuchang Gao**

Affiliation:
Department of Mathematics, University of Idaho, Moscow, Idaho 83844

Email:
fuchang@uidaho.edu

**Wenbo V. Li**

Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716

Email:
wli@math.udel.edu

DOI:
http://dx.doi.org/10.1090/S0002-9947-06-03963-8

Received by editor(s):
October 28, 2004

Received by editor(s) in revised form:
February 2, 2005

Published electronically:
October 16, 2006

Additional Notes:
The first author was supported in part by NSF Grants EPS-0132626 and DMS-0405855

The second author was supported in part by NSF Grant DMS-0204513

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.