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May 2022 Spectral equivalence of Gaussian random functions: Operator approach
Alexander Nazarov, Yakov Nikitin
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Bernoulli 28(2): 1448-1460 (May 2022). DOI: 10.3150/21-BEJ1396

Abstract

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.

Funding Statement

This work was supported by the Russian Foundation of Basic Research Grant 20-51-12004.

Acknowledgements

The authors are indebted to Professor I.A. Ibragimov, Professor M.A. Lifshits and anonimous referees for valuable comments and suggestions.

Citation

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Alexander Nazarov. Yakov Nikitin. "Spectral equivalence of Gaussian random functions: Operator approach." Bernoulli 28 (2) 1448 - 1460, May 2022. https://doi.org/10.3150/21-BEJ1396

Information

Received: 1 November 2020; Revised: 1 July 2021; Published: May 2022
First available in Project Euclid: 3 March 2022

Digital Object Identifier: 10.3150/21-BEJ1396

Keywords: Brownian sheet , Gaussian random functions , identity in law , spectral equivalence , tensor product

Rights: Copyright © 2022 ISI/BS

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Vol.28 • No. 2 • May 2022
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