• DOI:10.1017/S0027763000019759
• Corpus ID: 116988986

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}
}

• Kazuyuki Inoue, Akio Noda
• Published 1 March 1982
• Mathematics
• Nagoya Mathematical Journal

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|.