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Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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A Factorization problem and the problem of predicting non-stationary vector-valued stochastic processes

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Abstract

In this paper a prediction theory is developed under the general idea that the infinite dimensional covariance matrix is a self-adjoint element in a symmetric Banach algebra. The usual Wiener's spectral factorization method for solving stationary Wiener-Hopf equations has been extended to this algebra. Finally, a theorem for factoring a positive definite covariance matrix into upper and lower triangular factors with similar inverses has been proved. © 1969 Springer-Verlag.

Date

01 Sep 1969

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Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

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