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Journal of Multivariate Analysis 87 (2003) 133158 Wavelet methods for continuous-time prediction
 

Summary: Journal of Multivariate Analysis 87 (2003) 133­158
Wavelet methods for continuous-time prediction
using Hilbert-valued autoregressive processes
Anestis Antoniadisa,Ã
and Theofanis Sapatinasb
a
Laboratoire IMAG-LMC, 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 continuous-time stochastic process on an entire
time-interval 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 ill-posed
inverse problems. In the deterministic literature, such problems are usually solved by suitable
regularization techniques. We describe some recent approaches from the deterministic

  

Source: Antoniadis, Anestis - Laboratoire Jean Kuntzmann, Université Joseph Fourier
Sapatinas, Theofanis - Department of Mathematics and Statistics, University of Cyprus

 

Collections: Mathematics