Information and information stability of random variables and processes. Translated and edited by Amiel Feinstein. (Информация и информационная устойчивостьслучайных величин и процессов.) (English. Russian original) Zbl 0125.09202

Holden-Day Series in Time Series Analysis. San Francisco-London-Amsterdam: Holden-Day, Inc. xii, 243 p. (1964); translation from Problemy Peredachi Informatsii, Vyp. 7. Moskva: Izdat. Akad. Nauk SSSR, 203 p. (1960).
In this book (apparently based on a thesis) the author gives a strict and detailed account of the measure-theoretic foundations of information theory as applied to numerically valued random variables, and of the application of this theory to information theory of Gaussian random processes. The first four chapters deal with the basic theory of information and information stability relying heavily on the work of Dobrushin. The next four deal with information rate and stability for stationary random processes in general and discrete-parameter finite states whilst the last three chapters consider Gaussian random processes. The discussion is everywhere terse and succinct but many of the chapters are followed by helpful notes by the editor. This book embodies much information not easily found elsewhere.
A German translation has been published in 1963: Arbeiten zur Informationstheorie. V: Information und Informationsstabilität zufälliger Größen und Prozesse. Übersetzung aus dem Russischen von Kurt Nawrotzki. Verantwortlicher Lektor Brigitte Mai. Mathematische Forschungsberichte, XVIII. VEB Deutscher Verlag der Wissenschaften, Berlin 184 p. (1963).
Reviewer: P. A. P. Moran


94-02 Research exposition (monographs, survey articles) pertaining to information and communication theory
94A17 Measures of information, entropy
94A15 Information theory (general)
60G15 Gaussian processes
62B10 Statistical aspects of information-theoretic topics