X: 07, 86-103, LNM 511 (1976)
MEYER, Paul-André
La théorie de la prédiction de F. Knight (
General theory of processes)
This paper is devoted to the work of Knight,
Ann. Prob. 3, 1975, the main idea of which is to associate with every reasonable process $(X_t)$ another process, taking values in a space of probability measures, and whose value at time $t$ is a conditional distribution of the future of $X$ after $t$ given its past before $t$. It is shown that the prediction process contains essentially the same information as the original process (which can be recovered from it), and that it is a time-homogeneous Markov process
Comment: The results are related to those of Schwartz (presented in
722), the main difference being that the future is predicted instead of the whole path. Knight has devoted to this subject the
Essays on the Prediction Process, Hayward Inst. of Math. Stat., 1981, and a book,
Foundations of the Prediction Process, Oxford Science Publ. 1992
Keywords: Prediction theoryNature: Exposition,
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