A theory for multiscale stochastic realization

Describes a generalisation theory for a class of multiscale stochastic processes. This realisation problem represents a non-trivial variation on the standard time series stochastic realisation problem. The authors generalize some Gaussian Markov random fields representation results, thereby developing a fuller understanding of what types of stochastic phenomena can be usefully captured by the multiscale framework and how the corresponding models can be built. The authors´ theory for multiscale stochastic realization is based on a novel application of the techniques of canonical correlation analysis. These techniques, which rely heavily on the singular value decomposition, constitute a standard analytical tool in both multivariate statistics and in the field of reduced-order modeling of linear systems. Using canonical correlation theory, the authors demonstrate that any given l-D or 2-D Gaussian random process, Markov or otherwise, can be represented by some multiscale model. More importantly, the authors also introduce a family of approximate representations