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Independence of the increments of Gaussian random fields
Published online by Cambridge University Press: 22 January 2016
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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|.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1982
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