Equivalent Gaussian Distributions and their Densities

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


Let ξ = ξ(t) be a Gaussian random function of the parameter tΤ with values ξ (t) = ξ(ω,t), ω ∈ Ω, on a probability space (Ω, \( \mathfrak{A} \), P). We assume that the (σ-algebra \( \mathfrak{A} \) is generated by ξ (t) = ξ(w,t) on Ω as the parameter t runs through the set T; in particular, then, the probability measure P on the σ-algebra \( \mathfrak{A} \) = \( \mathfrak{A} \) ξ is Gaussian.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations