 
Summary: Journal of Multivariate Analysis 87 (2003) 133158
Wavelet methods for continuoustime prediction
using Hilbertvalued autoregressive processes
Anestis Antoniadisa,Ã
and Theofanis Sapatinasb
a
Laboratoire IMAGLMC, University Joseph Fourier, 51 rue de Mathematiques, BP 53, 38041
Grenoble Cedex 9, France
b
Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537,
CY 1678 Nicosia, Cyprus
Received 10 September 2001
Abstract
We consider the prediction problem of a continuoustime stochastic process on an entire
timeinterval in terms of its recent past. The approach we adopt is based on the notion of
autoregressive Hilbert processes that represent a generalization of the classical autoregressive
processes to random variables with values in a Hilbert space. A careful analysis reveals, in
particular, that this approach is related to the theory of function estimation in linear illposed
inverse problems. In the deterministic literature, such problems are usually solved by suitable
regularization techniques. We describe some recent approaches from the deterministic
