Expansions for Gaussian processes and Parseval frames

Details Expansions for Gaussian processes and Parseval frames Expansions for Gaussian processes and Parseval frames

2009-02-15

arxiv.org/abs/0902.2563v1

Mathematics

Probability

20 pages

Scientific paper

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.

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