Expansions for Gaussian Processes and Parseval Frames

Harald Luschgy (University of Trier)
Gilles Pagès (Université Paris 6)

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.

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Pages: 1198-1221

Publication Date: June 1, 2009

DOI: 10.1214/EJP.v14-649

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