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White noise approach to Gaussian random fields

Published online by Cambridge University Press:  22 January 2016

Ke-Seung Lee
Ke-Seung Lee*
Affiliation:
College of Liberal Arts and Sciences Department of Mathematics Korea University, Chochiwan, Korea
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The purpose of this paper is to investigate way of dependency of Gaussian random fields X(D) indexed by a domain D in d-dimensional Euclidean space Rd. Our main tool is variational calculus, where the boundary of a domain varies and deforms and we appeal to the white noise analysis. We therefore assume that X(D) is expressed white noise integral of the form

(0.1) X(D) = X(D, W)=∫D F(D, u)W(u)du,

where W is the Rd-parameter white noise and the kernel F(D, u) is a square integrable function over Rd, and where D is a bounded domain with smooth boundary.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 119 , September 1990 , pp. 93 - 106
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

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