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Reversibility and Identifiability

  • Murray Rosenblatt
Part of the Springer Series in Statistics book series (SSS)

Abstract

Let us first consider linear stationary sequences. A sequence of independent, identically distributed real random variables ξj, j = …, -1,0,1,… is given with Eξj = 0, 0 < Eξ j 2 = σ2 < ∞. The process xj is obtained by passing this sequence through a linear filter characterized by the real weights, a j , ∑a j 2 < ∞,
$$ {x_{t}} = \sum\limits_{{j = - \infty }}^{\infty } {{a_{j}}\xi t - j.} $$
(1.1.1)

Keywords

Spectral Density ARMA Process Real Random Variable Gaussian Stationary Sequence Countable Commutative Group 
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 2000

Authors and Affiliations

  • Murray Rosenblatt
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaSan Diego La JollaUSA

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