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The prediction theory of multivariate stochastic processes, II

The linear predictor

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Acta Mathematica

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Authors and Affiliations

  1. Cambridge, Mass., USA

    N. Wiener & P. Masani

  2. Bombay, India

    N. Wiener & P. Masani

Authors
  1. N. Wiener
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  2. P. Masani
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Additional information

This paper, like Part I [12], contains the research we carried out at the Indian Statistical Institute, Calcutta, during 1955–56, along with some simplifications resulting from later work. We would again like to thank the authorities for the excellent facilities placed at our disposal, and Dr.G. Kallianpur for valuable discussions.

Since writing this paper we have learned that some of our results in Part I have been duplicated byH. Helson andD. Lowdenslager, cf. their paper, “Prediction theory and Fourier series in several variables”, to be published in this volume ofActa Mathematica. We regret that no reference was made to this fact in Part I. In a recent note [Proc. Nat. Acad. Sci. U.S.A., Vol. 43 (1957) pp. 898–992]M. Rosenblatt has derived Theorem 7.10 proved by us in Part I, but his derivation is based on an incorrect lemma. To rectify this one would have to go through the steps followed in our Part I.

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Wiener, N., Masani, P. The prediction theory of multivariate stochastic processes, II. Acta Math. 99, 93–137 (1958). https://doi.org/10.1007/BF02392423

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