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On Non-Anticipative Linear Transformations of Gaussian Processes with Equivalent Distributions

Published online by Cambridge University Press:  22 January 2016

YU. A. Rozanov
YU. A. Rozanov*
Affiliation:
Steklov Mathematical Institute, Moscow
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Let ξ(t), t ∈ T, be a Gaussian process on a set T, and H = H(ξ) be the closed linear manifold generated by all values ξ(t), t ∈ T, with the inner product

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 47 , September 1972 , pp. 227 - 235
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

References

[1] Rozanov, Yu A., Infinite-dimensional Gaussian distributions (in Russian), Proc. Steklov Math. Inst., 108, 1968 (English translation Amer. Math. Soc, Providence, 1971).Google Scholar
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[4] Kallianpur, G. and Oodaira, H., Non-anticipative representations of equivalent Gaussian processes (in print).Google Scholar
[5] Kailath, T., Likelihood ratios of Gaussian processes, IEEE Trans. Information theory IT-16, 276–288, 1970.CrossRefGoogle Scholar
[6] Ibragimov, I. A. and Rozanov, Yu. A., Gaussian random processes (in Russian), M., “Nauka”, 1970.Google Scholar