Spectral characterization of the Wold–Zasuhin decomposition and prediction-error operator

Autor:	S. C. Power
Rok vydání:	1991
Předmět:	Stationary process Stochastic process General Mathematics Mathematical analysis Hilbert space Characterization (mathematics) Hermitian matrix symbols.namesake Operator (computer programming) Decomposition (computer science) symbols Algorithm Mathematics Toeplitz operator
Zdroj:	Mathematical Proceedings of the Cambridge Philosophical Society. 110:559-567
ISSN:	1469-8064 0305-0041
DOI:	10.1017/s0305004100070626
Popis:	Over thirty years ago Wiener and Masani pointed out in the introduction of their celebrated paper [31] that for a general multivariate stationary stochastic process no relation had been given for the prediction-error matrix in terms of the spectrum of the process. In particular it was unknown how to characterize the rank of the process in spectral terms (cf. Masani[12], p. 369, question 1). Despite explicit progress in this connection with certain regular processes, such as the series representations in [11, 19, 22, 32], or the iterative approach of [28, 29], and despite progress in the structure theory of degenerate processes ([8, 10, 14, 15, 26]), a general relation or series expression has remained elusive.
Databáze:	OpenAIRE
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