Electronic Journal of Probability

Expansions for Gaussian Processes and Parseval Frames

Harald Luschgy and Gilles Pagès

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We derive a precise link between series expansions of Gaussian random vectors in a Banach space and Parseval frames in their reproducing kernel Hilbert space. The results are applied to pathwise continuous Gaussian processes and a new optimal expansion for fractional Ornstein-Uhlenbeck processes is derived.

Article information

Electron. J. Probab., Volume 14 (2009), paper no. 42, 1198-1221.

Accepted: 1 June 2009
First available in Project Euclid: 1 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G15: Gaussian processes
Secondary: 42C15: General harmonic expansions, frames

Gaussian process series expansion Parseval frame optimal expansion fractional Ornstein-Uhlenbeck process

This work is licensed under aCreative Commons Attribution 3.0 License.


Luschgy, Harald; Pagès, Gilles. Expansions for Gaussian Processes and Parseval Frames. Electron. J. Probab. 14 (2009), paper no. 42, 1198--1221. doi:10.1214/EJP.v14-649. https://projecteuclid.org/euclid.ejp/1464819503

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