B. Tsirelson

Spectral densities describing off-white noises

Recent works

Boris Tsirelson,
"Spectral densities describing off-white noises."
Annales de l'Institut Henri Poincare Probabilites et Statistiques 38:6, 1059-1069 (2002).
Available online from Elsevier (not free, sorry; if refused by Elsevier, use arXiv or ask me for reprint):

Also available online (free of charge) from e-print archive (USA):
or its Israeli mirror:

A research paper, 12 pages, bibl. 6 refs.

For the white noise, the spectral density is constant, and the past (restriction to (-infinity,0)) is independent from the future (restriction to (0,+infinity)). If the spectral density is not too far from being constant, then dependence between the past and the future can be eliminated by an equivalent measure change; that is called an off-white noise. I derive from well-known results a necessary and sufficient condition for a spectral density to describe an off-white noise.

  1. Introduction.
  2. Analytic functions inside and outside the circle.
  3. Generalized random processes in continuous time.
  4. Off-white noises.
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