Title: Consistency of the plug-in functional predictor of the Ornstein-Uhlenbeck process in Hilbert and Banach spaces,
Abstract: New results on functional prediction of the Ornstein-Uhlenbeck process in an
autoregressive Hilbert-valued and Banach-valued frameworks are derived.
Specifically, consistency of the maximum likelihood estimator of the
autocorrelation operator, and of the associated plug-in predictor is obtained
in both frameworks.