Expansions for Gaussian processes and Parseval frames

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.
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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>
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Harald Luschgy, Gilles Pagès. Expansions for Gaussian processes and Parseval frames. 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>. <hal-00361433>

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