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Conditional orthogonality and conditional stochastic realization

Caines, Peter E., Deardon, R. and Wynn, Henry P. ORCID: 0000-0002-6448-1080 (2002) Conditional orthogonality and conditional stochastic realization. In: Directions in mathematical systems theory and optimization. Lecture Notes in Control and Information Sciences (286). Springer-Verlag Berlin Heidelberg, Berlin, Germany, pp. 71-84. ISBN 9783540000655

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The concept of conditional orthogonality for the random variables x, y with respect to a third random variable z is extended to the case of a triple x, y, z of processes and is shown to be equivalent to the property that the space spanned by the conditioning process z splits the spaces generated by the conditionally orthogonal processes x, y. The main result is that for jointly wide sense stationary processes x, y, z, conditional orthogonality plus a strong feedback free condition on (z, x) and (z, y), or, equivalently, splitting plus this condition, is equivalent to the existence of a stochastic realization for the joint process (x, y, z) in the special class of so-called conditionally orthogonal stochastic realizations.

Item Type: Book Section
Official URL:
Additional Information: © 2002 Springer-Verlag Berlin Heidelberg
Divisions: Centre for Analysis of Time Series
Subjects: Q Science > QA Mathematics
Date Deposited: 05 Mar 2014 09:24
Last Modified: 01 Nov 2021 00:03

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