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2009 Expansions for Gaussian Processes and Parseval Frames
Harald Luschgy, Gilles Pagès
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Electron. J. Probab. 14: 1198-1221 (2009). DOI: 10.1214/EJP.v14-649


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.


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Harald Luschgy. Gilles Pagès. "Expansions for Gaussian Processes and Parseval Frames." Electron. J. Probab. 14 1198 - 1221, 2009.


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

zbMATH: 1195.60056
MathSciNet: MR2511282
Digital Object Identifier: 10.1214/EJP.v14-649

Primary: 60G15
Secondary: 42C15

Keywords: fractional Ornstein-Uhlenbeck process , Gaussian process , optimal expansion , Parseval frame , series expansion

Vol.14 • 2009
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