I'm looking for a reference for the Wold–Zasukhin decomposition in continuous time for stationary random processes on the real line. I am aware of the classic result in the book from Rozanov, which casts it as an integral with respect to a random measure, but I would like to know if it is possible to get it as a corollary of the Wold decomposition for isometric linear operators on Hilbert spaces, or a suitable corollary, instead of relying on spectral ideas and results.
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