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Distributions of stable random fields of Chentsov type

Published online by Cambridge University Press:  22 January 2016

Yumiko Sato
Yumiko Sato*
Affiliation:
Department of General Education, Aichi Institute of Technology Yakusa-cho, Toyota 470-03, Japan
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In this paper we discuss the determinism of distributions of some stable random fields which are constructed through integral-geometric method. The determinism depends on the dimension of the parameter space Rd.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 123 , September 1991 , pp. 119 - 139
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

[ 1 ] Chentsov, N. N., Lévy’s Brownian motion of several parameters and generalized white noise, Theory Probab. Appl., 2 (1957), 265–266.Google Scholar
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[ 3 ] Levy, P., Processus stochastiques et mouvement brownien, Gauthier-Villers, Paris. (1965, 2ème edition)Google Scholar
[ 4 ] Sato, Y., Joint distributions of some self-similar stable processes, preprint (1989).Google Scholar
[ 5 ] Sato, Y., Structure of Levy measures of stable random fields of Chentsov type, preprint (1990).Google Scholar
[ 6 ] Sato, Y. and Takenaka, S., On stable processes of Chentsov type, preprint (1990).Google Scholar
[ 7 ] Takenaka, S., Integral-geometric constructions of self-similar stable processes, Nagoya Math. J., 123 (1991),Google Scholar