Expansions for Gaussian processes and Parseval frames

Harald Luschgy; Gilles Pagès

doi:10.1214/EJP.v14-649

Expansions for Gaussian processes and Parseval frames

Harald Luschgy ¹ Gilles Pagès ²

2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

Abstract : 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. In the end an extension of this result to Gaussian stationary processes with convex covariance function is established.

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

Document type :

Journal articles

Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2009, 14 (42), 1198-1221 ; http://dx.doi.org/10.1214/EJP.v14-649. 〈10.1214/EJP.v14-649〉

Domain :

Mathematics [math] / Probability [math.PR]

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Contributor : Gilles Pagès <>
Submitted on : Sunday, February 15, 2009 - 2:07:22 PM
Last modification on : Tuesday, October 11, 2016 - 1:45:09 PM
Document(s) archivé(s) le : Tuesday, June 8, 2010 - 8:49:11 PM

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