Complete Regularity and Processes with Continuous Time

  • I. A. Ibragimov
  • Y. A. Rozanov
Part of the Applications of Mathematics book series (SMAP, volume 9)


We shall investigate in this section spectral characteristics of completely regular stationary processes ξ(t) with continuous time t,−∞ < t < ∞. In Section IV.1 we obtained a characterization of the spectrum of Gaussian stationary processes satisfying a strong mixing condition. We note in advance that the results regarding the behavior of spectral densities f(λ) of completely regular processes with continuous time on any finite interval of variation of λ are completely analogous to the results obtained in Chapter V for processes with discrete time. Specific difficulties arise only in the case of f(λ) as λ → ∞; unfortunately, the investigation of this case is less complete, although Theorems 5 and 6 do give some idea about phenomena arising here (see Sections VI.5 and VI.6).


Spectral Density Entire Function Unit Sphere Continuous Time Regular Function 
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Copyright information

© Springer-Verlag New York Inc. 1978

Authors and Affiliations

  • I. A. Ibragimov
    • 1
  • Y. A. Rozanov
    • 2
  1. 1.LomiLeningradUSSR
  2. 2.V.A. Steklov Mathematics InstituteMoscowUSSR

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