We introduce a new approach to the spectral equivalence of Gaussian processes and fields, based on the methods of operator theory in Hilbert space. Besides several new results including identities in law of quadratic norms for integrated and multiply integrated Gaussian random functions we give an application to goodness-of-fit testing.
This work was supported by the Russian Foundation of Basic Research Grant 20-51-12004.
The authors are indebted to Professor I.A. Ibragimov, Professor M.A. Lifshits and anonimous referees for valuable comments and suggestions.
"Spectral equivalence of Gaussian random functions: Operator approach." Bernoulli 28 (2) 1448 - 1460, May 2022. https://doi.org/10.3150/21-BEJ1396