Model reduction, optimal prediction, and the Mori-Zwanzig representation of Markov chains

Model reduction methods from diverse fields—including control, statistical mechanics and economics—aimed at systems that can be represented by Markov chains, are discussed in terms of their general properties and common features. These methods include decomposability, optimal prediction techniques, and Mori-Zwanzig representations. Our objective in this paper is to present a survey of and highlight connections between the approaches pursued in different fields, and demonstrate application of the methods on a set of well-known examples.

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