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 Berlin / Heidelberg, Berlin, Germany, pp. 71-84.
ISBN 9783540000655
Abstract
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: | http://link.springer.com/book/10.1007/3-540-36106-... |
| 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: | 15 Sep 2023 09:01 |
| URI: | http://eprints.lse.ac.uk/id/eprint/55990 |
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