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 Probability Surveys > Vol. 9 (2012) open journal systems 

Multivariate prediction and matrix Szegö theory

Nicholas H. Bingham, Imperial College, London

Following the recent survey by the same author of Szegö's theorem and orthogonal polynomials on the unit circle (OPUC) in the scalar case, we survey the corresponding multivariate prediction theory and matrix OPUC (MOPUC).

AMS 2000 subject classifications: Primary 60G10; secondary 60G25.

Keywords: Stationary process, vector-valued, multivariate prediction theory, multivariate orthogonal polynomials on the unit circle (MOPUC), Kolmogorov isomorphism theorem, Verblunsky’s theorem, Szegö’s theorem.

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Bingham, Nicholas H., Multivariate prediction and matrix Szegö theory, Probability Surveys, 9, (2012), 325-339 (electronic). DOI: 10.1214/12-PS200.


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