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.
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Caines, P.E., Deardon, R., Wynn, H.P. (2003). Conditional Orthogonality and Conditional Stochastic Realization. In: Rantzer, A., Byrnes, C.I. (eds) Directions in Mathematical Systems Theory and Optimization. Lecture Notes in Control and Information Sciences, vol 286. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36106-5_6
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DOI: https://doi.org/10.1007/3-540-36106-5_6
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