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On the structure of splitting fields of stationary Gaussian processes with finite multiple Markovian property

Published online by Cambridge University Press:  22 January 2016

Yasunori Okabe
Yasunori Okabe*
Affiliation:
Nagoya University
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Let X = (X(t); t ∈ R) be a real stationary mean continuous Gaussian process with expectation zero which is purely nondeterministic. In this paper we shall investigate the structure of splitting fields of X having finite multiple Markovian property using the results in [6]. We follow the notations and terminologies in [6].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 54 , July 1974 , pp. 191 - 213
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

References

[1] Doob, J. L.: The elementary Gaussian processes, Ann. Math. Statist. 15 (1944), 229–282.Google Scholar
[2] Dym, H.: Stationary measures for the flow of a linear differential equation driven by white noise, Trans. Amer. Math. Soc. 123 (1966), 130–164.CrossRefGoogle Scholar
[3] Hida, T.: Canonical representations of Gaussian processes and their applications, Mem. Coll. Sci. Univ. Kyoto, Ser. A, Math. 34 (1960), 109–155.Google Scholar
[4] Hörmander, L.: Hypoelliptic second order differential equations, Acta Math. 119 (1967), 141–171.CrossRefGoogle Scholar
[5] Levinson, N. and McKean, H. P. Jr.: Weighted trigonometrical approximation on R1 with application to the germ field of a stationary Gaussian noise, Acta Math. 112 (1964), 99–143.Google Scholar
[6] Okabe, Y.: Stationary Gaussian processes with Markovian property and M. Sato’s hyperfunctions, to appear in Japanese J. of Math., 41 (1973), 69–122.Google Scholar