# Independence of the increments of Gaussian random fields

@article{Inoue1982IndependenceOT, title={Independence of the increments of Gaussian random fields}, author={Kazuyuki Inoue and Akio Noda}, journal={Nagoya Mathematical Journal}, year={1982}, volume={85}, pages={251 - 268} }

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|.

## 10 Citations

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### Representation of Euclidean Random Field

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