The Annals of Probability

The Supremum of a Particular Gaussian Field

Robert J. Adler

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Abstract

We find exact upper and lower bounds for the distribution of the supremum of a homogeneous Gaussian random field with pyramidal covariance function. The upper bound comes from a reflection principle type argument. The lower bound is found by exploiting a relationship between this random field and a particular Banach space valued process in one-dimensional time.

Article information

Source
Ann. Probab., Volume 12, Number 2 (1984), 436-444.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993299

Digital Object Identifier
doi:10.1214/aop/1176993299

Mathematical Reviews number (MathSciNet)
MR735847

Zentralblatt MATH identifier
0541.60034

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60G60: Random fields 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11] 60G17: Sample path properties

Keywords
Random field pyramidal covariance supremum

Citation

Adler, Robert J. The Supremum of a Particular Gaussian Field. Ann. Probab. 12 (1984), no. 2, 436--444. doi:10.1214/aop/1176993299. https://projecteuclid.org/euclid.aop/1176993299


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