Prediction and design
Let \(\{X_ t\), \(t\in T\}\) be a random process, and let S be a finite subset of T. Define \(E^ SX_ t=E(X_ t| X_ s\), \(s\in S)\). If for any t and S, \(E^ SX_ t=\sum p^ S_ t(s)X_ S\), where \(p^ S_ t(s)\geq 0\) and \(\sum p^ S_ t(s)\leq 1\), then \(\{X_ t\}\) is called a G-MAP (Gaussian, Markov-associated process). The author gives several examples of G-MAPs and studies their properties. One of the most important problems is the choice of S such that \(| S| =n\) and the error process \(\{X_ t-E^ SX_ t\), \(t\in T\}\) is in some sense minimal. It leads to natural prediction and design questions. The case of a process observed with error is also considered.
scientific article; zbMATH DE number 4054858