Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

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
Laboratoire IMAG-LMC, University Joseph Fourier, 51 rue de Mathematiques, BP 53, 38041
Grenoble Cedex 9, France
Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537,
CY 1678 Nicosia, Cyprus
Received 10 September 2001
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