Abstract
Let us consider a stationary narrow-sense random process ξ(t) with continuous or discrete time t. We denote, as before, by \( \mathfrak{A} \)(T) the σ-algebra of events generated by the process on the set T, that is, \( \mathfrak{A} \) (T) is the minimal σ-algebra containing events such as
the E j being Borel sets on the real line.* Algebras of the form \( \mathfrak{A} \)(−∞, t) determine the past of the process (before time t), algebras of the form \( \mathfrak{A} \)(t, ∞) determine the future of the process (after time t).
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© 1978 Springer-Verlag New York Inc.
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Ibragimov, I.A., Rozanov, Y.A. (1978). Conditions for Regularity of Stationary Random Processes. In: Gaussian Random Processes. Applications of Mathematics, vol 9. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6275-6_4
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DOI: https://doi.org/10.1007/978-1-4612-6275-6_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6277-0
Online ISBN: 978-1-4612-6275-6
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