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.