Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-18T18:23:08.912Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[ 1 ] Aczél, J., Lectures on Functional Equations and Their Applications, Academic Press, New York and London, 1966.Google Scholar
[ 2 ] Levy, P., Processus Stochastiques et Mouvement Brownien, Gauthier-Villars, Paris, 1965.Google Scholar
[ 3 ] Noda, A., Gaussian random fields with projective invariance, Nagoya Math. J., 59 (1975), 65–76.Google Scholar
[ 4 ] Schoenberg, I.J., Metric spaces and completely monotone functions, Annals of Math., 39 (1938), 811–841.Google Scholar
[ 5 ] Widder, D., The Laplace Transform, Princeton, New Jersey, 1946.Google Scholar
[ 6 ] Yaglom, A.M., Some classes of random fields in n-dimensional space related to stationary random processes, Theory Prob. Appl., 2 (1957), 273–320 (English translation).Google Scholar