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.
"Expansions for Gaussian Processes and Parseval Frames." Electron. J. Probab. 14 1198 - 1221, 2009. https://doi.org/10.1214/EJP.v14-649