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Innovation processes associated with stationary Gaussian processes with application to the problem of prediction

Published online by Cambridge University Press:  22 January 2016

Yasunori Okabe
Yasunori Okabe*
Affiliation:
Department of Mathematics Faculty of Science, University of Tokyo Hongo, Tokyo, Japan
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As a continuation of the previous paper [7], we shall consider in this paper the problem of prediction given bounded intervals and obtain integral representations of predictors and prediction errors. For that purpose we shall introduce innovation processes well matched with bounded intervals. We follow the notation and terminology in [6].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 70 , July 1978 , pp. 81 - 104
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

References

[1] Dym, H. and McKean, H. P. Jr.: Application of de Branges spaces of integral functions to the prediction of stationary Gaussian processes, Illinois J. Math. 45 (1970), 299–343.Google Scholar
[2] Dym, H. and McKean, H. P. Jr.: Gaussian processes, Function Theory, and the Inverse Spectral Problem, Academic Press, New York, 1976.Google 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] Kailath, T.: A note on least squares estimation by the innovation method, SIAM J. Control 10 (1972), 477–486.CrossRefGoogle Scholar
[5] Kallianpur, G., Fujisaki, M. and Kunita, H.: Stochastic differential equations for the nonlinear filtering problem, Osaka J. Math. 9 (1972), 19–40.Google Scholar
[6] Okabe, Y.: Stationary Gaussian processes with Markovian property and M. Sato’s hyperfunctions, Japanese J. of Math. 41 (1973), 69–122.CrossRefGoogle Scholar
[7] Okabe, Y.: On the structure of splitting fields of stationary Gaussian processes with finite multiple Markovian property, Nagoya Math. J. 54 (1974), 191–213.CrossRefGoogle Scholar