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Conditional orthogonality and conditional stochastic realization
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UNSPECIFIED (2003) Conditional orthogonality and conditional stochastic realization. DIRECTIONS IN MATHEMATICAL SYSTEMS THEORY AND OPTIMIZATION, 286 . pp. 71-84. ISSN 0170-8643.
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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: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software T Technology > TL Motor vehicles. Aeronautics. Astronautics |
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Series Name: | LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES | ||||
Journal or Publication Title: | DIRECTIONS IN MATHEMATICAL SYSTEMS THEORY AND OPTIMIZATION | ||||
Publisher: | SPRINGER-VERLAG BERLIN | ||||
ISSN: | 0170-8643 | ||||
Official Date: | 2003 | ||||
Dates: |
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Volume: | 286 | ||||
Number of Pages: | 14 | ||||
Page Range: | pp. 71-84 | ||||
Publication Status: | Published |
Data sourced from Thomson Reuters' Web of Knowledge
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