Abstract
The relationship between a physical model and a time series model (or an innovation model) is discussed from the viewpoint of contraction of information due to the way of observation. In this framework, measurable correlation functions are expressed in terms of both models. By using the Riccati type equation and the singular value decomposition of the Hankel matrix, a data-oriented model is derived from measurable correlation functions. There occurs the contraction in a noise source space (or random forces). From the mechanism of contraction, random forces of systems can be identified by using two innovation models in different states.
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