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Independence of the increments of Gaussian random fields

Published online by Cambridge University Press:  22 January 2016

Kazuyuki Inoue  and
Akio Noda
Kazuyuki Inoue
Affiliation:
Department of Mathematics, Shinshu University
Akio Noda
Affiliation:
Department of Mathematics, Aichi University of Education
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Let be a mean zero Gaussian random field (n ⋜ 2). We call X Euclidean if the probability law of the increments X(A) − X(B) is invariant under the Euclidean motions. For such an X, the variance of X(A) − X(B) can be expressed in the form r(|A − B|) with a function r(t) on [0, ∞) and the Euclidean distance |A − B|.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 85 , March 1982 , pp. 251 - 268
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

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