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Representation of Euclidean Random Field

Published online by Cambridge University Press:  22 January 2016

Shigeo Takenaka
Shigeo Takenaka*
Affiliation:
Department of Mathematics Nagoya University, Chikusa-ku, Nagoya 464, Japan
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P. Lévy introduced a notion of Brownian motion with parameter in a metric space (M, d), which is a centered Gaussian system satisfying

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 105 , March 1987 , pp. 19 - 31
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

[ 1 ] Chentsov, N. N., Lévy’s Brownian motion of several parameters and generalized white noise, Theory Probab. Appl., 2 (1957), 265–266.CrossRefGoogle Scholar
[ 2 ] Deans, S. R., A unified Radon inversion formula, J. Math. Phys., 19 (1978), 2346–2349.Google Scholar
[ 3 ] Gangolli, R., Positive definite kernels on homogeneous spaces and certain stochastic processes related to Lévy’s Brownian motion of several parameters, Ann. Inst. H. Poincaré Sect. B, 3 (1967), 121–226.Google Scholar
[ 4 ] Inoue, K. and Noda, A., Independence of the increments of Gaussian random fields, Nagoya Math. J., 85 (1982), 251–268.Google Scholar
[ 5 ] Levy, P., Processus stochastiques et mouvement brownien, Gauthier-Villars (1965).Google Scholar
[ 6 ] Lifshits, M. A., On representation of Levy’s field by indicators, Theory Probab. Appl., 24 (1979), 629–633.Google Scholar
[ 7 ] Molcan, G. M., Markov property of Levy’s fields on spaces of constant curvature, Dokl. Akad. Nauk CCCP, torn. 221 (1975), 1276-1279.Google Scholar
[ 8 ] Noda, A., Integral transformation, associated with Levy’s Brownian motion, Tech. Rep. Univ. Erlangen (1984).Google Scholar
[ 9 ] Pflug, G., A statistically important Gaussian process, Stochastic Process. Appl., 13 (1982), 45–57.Google Scholar
[10] Takenaka, S., Kubo, I. and Urakawa, H., Brownian motion parametrized with metric space of constant curvature, Nagoya Math. J., 82 (1981), 131–140.Google Scholar
[11] Mandelbrot, B., Fonctions aléatoires plurei-temporelles; approximation poissonienne de cas brownien et généralisations, C.R. Acad. Se. Paris, 280A (1975), 1075-1078.Google Scholar
[12] Noda, A., Generalized Radon transform and Lévy’s Brownian motion I, II, Nagoya Math. J., 105 (1987), 71-87, 89–107.Google Scholar
[13] Ossiander, M. and Pyke, R., Lévy’s Brownian motion as a set-indexed process and a related central limit theorem, Stochastic Process. Appl., 21 (1985), 133–145.Google Scholar