Caines, Peter E., Deardon, R. and Wynn, Henry P. (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
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 |
| Library of Congress subject classification: | Q Science > QA Mathematics |
| Sets: | Research centres and groups > Centre for the Analysis of Time Series (CATS) Research centres and groups > Decision Support and Risk Group (DSRG) |
| Date Deposited: | 05 Mar 2014 09:24 |
| URL: | http://eprints.lse.ac.uk/55990/ |
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