Hilbert Spaces

  • Peter J. Brockwell
  • Richard A. Davis
Part of the Springer Series in Statistics book series (SSS)

Abstract

Although it is possible to study time series analysis without explicit use of Hilbert space terminology and techniques, there are great advantages to be gained from a Hilbert space formulation. These are largely derived from our familiarity with two- and three-dimensional Euclidean geometry and in particular with the concepts of orthogonality and orthogonal projections in these spaces. These concepts, appropriately extended to infinite-dimensional Hilbert spaces, play a central role in the study of random variables with finite second moments and especially in the theory of prediction of stationary processes.

Keywords

Hilbert Space Conditional Expectation Cauchy Sequence Closed Subspace Prediction Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • Peter J. Brockwell
    • 1
  • Richard A. Davis
    • 1
  1. 1.Department of StatisticsColorado State UniversityFort CollinsUSA

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