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Variation principle in informational macrodynamics. (English) Zbl 1058.94007

The Kluwer International Series in Engineering and Computer Science 736. Boston, MA: Kluwer Academic Publishers (ISBN 1-4020-7465-4/hbk). xi, 264 p. (2003).
The book under review is devoted to the modelling of various information processes. The subject belongs to an interdisciplinary science, and the results are based on stochastic analysis and the calculus of variations technique. The model reveals information regularities and is called an information macrodynamics (IMD). The IMD model applies to observed objects already represented by a random Markovian process, considered as an initial model’s microprocess. The IMD model is based on a minimax variation principle which selects from the observed microprocess the most probable and nonredundant dynamic trajectories called the macroprocess. The minimax variation principle produces equations with optimal control functions and applies to both the observed object and its macromodel approximating the microlevel process by the macrolevel process with a minimal uncertainty. The book consists of three parts. Part 1 contains a conceptual review of the IMD basic results. Part 2 contains the mathematical foundation of the IMD. Some mathematical details, proofs and results are published for the first time. The last part contains some applications of the IMD to problems in intelligence systems, macroeconomics, biological systems and some other areas.

MSC:

94A15 Information theory (general)
60H30 Applications of stochastic analysis (to PDEs, etc.)
60H07 Stochastic calculus of variations and the Malliavin calculus
94A17 Measures of information, entropy