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References
V.M. Adamjan and D.Z. Arov, On unitary couplings of semi-unitary operators, Amer. Math. Soc. Transl. (2) vol. 95, 1970, p.75–129.
V.M. Adamjan, D.Z. Arov and M.G. Krein, Infinite Hankel block matrices and related extension problems, Amer. Math. Soc. Transl. (2) vol. 111, 1978, p.133–156.
H. Akaike, Stochastic theory of minimal realizations, I.E.E.E. Trans. Automatic Control, Ac-19, 1974, p.667–674.
H. Dym and H.P. McKean, Gaussian Processes, Function Theory, and the Inverse Spectral Problem, Academic Press, New York, 1976.
P.A. Fuhrmann, Linear Operators and Systems in Hilbert Space, McGraw-Hill, New York, 1981.
I.M. Gelfand and A.M. Yaglom, Calculation of the amount of information about a random function contained in another such function, Amer. Math. Soc. Transl. (2) vol. 12, 1959, p.199–246.
I.C. Gohberg and M.G. Krein, Introduction to the theory of linear non selfadjoint operators, Translation of Math. Monographs, vol. 18, Amer. Math. Soc., Providence, R.I., 1969.
H. Helson, Lectures on invariant subspaces, Academic Press, New York, 1964.
H. Helson and G. Szegö, A problem in prediction theory, Ann. Mat. Pura App. 51, 1960, p.107–138.
H. Helson and D.E. Sarason, Past and future, Math. Scand. 21, 1967, p.5–16. Addendum by D.E. Sarason, Math. Scand. 30, 1972, p. 62–64.
I.A. Ibragimov and Y.A. Rozanov, Gaussian Random Processes, Springer, New York, 1978.
N.P. Jewell and P. Bloomfield, Canonical correlations of past and future for time series: definitions and theory, Ann. Statist. 11, 1983, p.837–847.
N.P. Jewell, P. Bloomfield and F.C. Bartmann, Canonical correlations of past and future for time series: bounds and computation, Ann. Statist. 11, 1983, p.848–855.
E.A. Jonckheere and J.W. Helton, Power spectrum reduction by optimal Hankel norm approximation of the phase of the outer spectral factor, Proc. Amer. Control Conf., San Diego, CA, June 1984.
S. Kullback, Information Theory and Statistics, Dover, New York, 1968.
P.D. Lax and R.S. Phillips, Scattering Theory, Academic Press, New York, 1967.
A. Lindquist and G. Picci, State space models for Gaussian stochastic processes; in Stochastic Systems: The Mathematics of Filtering and Identification and Applications, M. Hazewinkel and J.C. Willems Eds., Reidel Publ. Co. Dordrecht, 1981, p.169–204.
A. Lindquist, M. Pavon and G. Picci, Recent trends in stochastic realization theory, in Prediction Theory and Harmonic Analysis — The Pesi Masani Volume, V. Mandrekar and H. Salehi Eds., North Holland, Amsterdam, 1983, p.201–224.
S.K. Mitter, Personal communication, 1980 and talk delivered at this conference.
J. Neveu, Processus Aléatoires Gaussiens, Presses de l'Université de Montréal, 1968.
L.B. Page, Bounded and compact vectorial Hankel operators, Trans. Amer. Math. Soc. 150, 1970, p.529–539.
M. Pavon, Canonical correlations of past inputs and future outputs for linear stochastic systems, Systems & Control Letters 4, 1984, p.209–215.
V.V. Peller and S.V. Khrushchev, Hankel operators, best approximations, and stationary Gaussian processes, Russian Math. Surveys 37, 1982, p.61–144.
M. Rosenblatt, A central limit theory and a strong mixing condition, Proc. Nat. Acad. Sci. U.S.A. 42, 1956, p.43–47.
Y.A. Rozanov, Stationary Random Processes, Holden-Day, San Francisco, 1967.
G. Ruckebusch, Théorie géométrique de la Représentation Markovienne, Ann. Inst. Henri Poincaré, Section B, XVI, 1980, p.225–297.
G. Ruckebusch, Markovian representations and spectral factorizations of stationary Gaussian processes, in Prediction Theory and Harmonic Analysis — The Pesi Masani Volume, V. Mandrekar and H. Salehi Eds., North Holland, Amsterdam, 1983, p.275–307.
A.M. Yaglom, Stationary Gaussian processes satisfying the strong mixing and best predictable functionals, Proc. Int. Research Seminar of the Statistical Laboratory, Univ. of Calif. Berkeley, 1963, p.241–252, Springer-Verlag, New York.
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© 1986 International Institute for Applied Systems Analysis
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Pavon, M. (1986). Canonical correlations, hankel operatiors and markovian representations of multivariate stationary Gaussian processes. In: Arkin, V.I., Shiraev, A., Wets, R. (eds) Stochastic Optimization. Lecture Notes in Control and Information Sciences, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007093
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DOI: https://doi.org/10.1007/BFb0007093
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