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Original Articles

Information macrodynamic modelling of a random process

Pages 729-744 | Received 24 Jan 2008, Accepted 11 Nov 2008, Published online: 24 Jun 2009

References

  • Alekseev , VM , Tichomirov , VM and Fomin , SV . 1979 . Optimal Control , Moscow : Nauka .
  • Andronov , AA , Witt , AA and Pontryagin , LS . 1933 . About Statistical Approach to Dynamic Systems . Journal of Experimental and technical physics , 3 : 165 – 180 . [Academy of Science, Moscow]
  • Astrom , K . 1970 . Introduction to Stochastic Control Theory , New York : Academic Press .
  • Balakrishnan , AV . 1972 . Stochastic Control: A Function Space Approach . SIAMI on Control , 10 : 285 – 297 .
  • Bellman , R . 1960 . Introduction to Matrix Analysis , New York : McGraw-Hill .
  • De Groot S.R. (ed.) (1960), Thermodynamics of Irreversible Processes, Bologna: International Physic School “Enrico Fermi”
  • Durr , D and Bach , A . 1978 . The Onsager–Machlup Function as Lagrangian for the Most Probable Path of Diffusion Process . Communications in Mathematical Physics , 60 : 153 – 170 .
  • Feldbaum , AA . 1961 . Theory of Dual control . Journal of Automatic and Telemechanics , 21 : 1240 – 1249 . 11:1453–1464, 22, 3–16, 2:129–142, [Moscow]
  • Feynman , RP . 1963 . The Character of Physical Law , London : Cox and Wyman Ltd .
  • Feynman , RP and Hibbs , AR . 1965 . Path Integral and Quantum Mechanics , New York : McGraw-Hill .
  • Fleming , WH and Rishel , RW . 1975 . Deterministic and Stochastic Optimal Control , New York : Springer-Verlag .
  • Fredlin , MI and Wentzell , AD . 1984 . Random Perturbations of Dynamic Systems , New York : Springer-Verlag .
  • Gelfand , IM and Fomin , SV . 1963 . Calculus of Variations , New York : Prentice Hall .
  • Gihman , II and Scorochod , AV . 1975 . Theory of Stochastic Processes , Vol. 3 , Moscow : Nauka .
  • Kalman , RRE and Bucy , RS . 1961 . New Results in Linear Filtering and Prediction Theory . Transactions of the ASME , 83 : 95 – 108 .
  • Kolmogorov , AN . 1987 . Theory of Information and Theory of Algorithms , Moscow : Nauka .
  • Kolmogorov , AN and Fomin , SV . 1981 . Elements of the Function's Theory and Functional Analysis , Moscow : Nauka .
  • Komoike , N . 1991 . Operator Ordering in Stochastic Hamiltonian and Path Integral Formalism of Stochastic Quantization . Progress of Theoretical Physics , 86 : 575 – 579 .
  • Lerner , VS and Roychel , BZ . 1989 . “ Building the Dynamic Model of a Random Object and the Solution of Control Problem ” . In Dynamics of Systems: Control and Optimization , Edited by: Neymark , YI . 41 – 58 . Gorki : GSU-press .
  • Lerner , VS . 1999 . Information Systems Analysis and Modeling: An Informational Macrodynamics Approach , Boston : Kluwer Academic Publishers .
  • Lerner , VS . 2003 . Variation Principle in Informational Macrodynamics , Boston : Kluwer Academic Publishers .
  • Lerner , VS . 2004 . Introduction to Information Systems Theory: Concepts, Formalism and Applications . International Journal of Systems Science , 35 : 405 – 424 .
  • Lerner , VS . 2007 . Dynamic Approximation of a Random Information Functional . Journal of Mathematical Analysis and Applications , 327 ( 1 ) : 494 – 514 .
  • Lerner , VS . 2008a . Cooperative Information Space Distributed Macromodels . International Journal of Control , 81 ( 5 ) : 725 – 751 .
  • Lerner , VS . 2008b . Macrodynamic cooperative complexity in Information Dynamics . Journal of Open Systems and Information Dynamics , 15 ( 3 ) : 231 – 279 .
  • Lerner , VS . 2009 . The boundary value problem and the Jensen inequality for an entropy functional of a Markov diffusion process . Journal of Mathematical Analysis and Applications , 353 ( 1 ) : 154 – 160 .
  • Shannon , CE and Weaver , W . 1949 . The Mathematical Theory of Communication , Urbana : The University of Illinois Press .
  • Stratonovich , RL . 1966 . The Conditional Marcovian Processes and their Applications in Optimal Control Theory , Moscow : Moscow University Press .
  • Stratonovich , RL . 1975 . Theory of Information , Moscow : Soviet Radio .
  • Talay , D . 2002 . Stochastic Hamiltonian Dissipative Systems: Exponential Convergence to the Invariant Measure, and Discretization by the Implicit Euler Scheme . Markov Processes and Related Fields , 8 : 163 – 198 .
  • Wiener , N . 1948 . Cybernetics , New York : John Wiley & Sons .
  • Zadeh , LA . 1953 . Optimum nonlinear filters . Journal of Applied Physics , 24 ( 4 ) : 396 – 404 .

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