Abstract
Let ξ = ξ(t) be a Gaussian random function of the parameter t ∈ Τ 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.
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© 1978 Springer-Verlag New York Inc.
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Ibragimov, I.A., Rozanov, Y.A. (1978). Equivalent Gaussian Distributions and their Densities. In: Gaussian Random Processes. Applications of Mathematics, vol 9. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6275-6_3
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DOI: https://doi.org/10.1007/978-1-4612-6275-6_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6277-0
Online ISBN: 978-1-4612-6275-6
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