Construction and analysis of probability models for controlled evolutionary systems
Author:
M. A. Fedotkin
Translated by:
V. Zaiats
Journal:
Theor. Probability and Math. Statist. 85 (2012), 133-147
MSC (2010):
Primary 60K99, 93C99
DOI:
https://doi.org/10.1090/S0094-9000-2013-00880-1
Published electronically:
January 14, 2013
MathSciNet review:
2933709
Full-text PDF Free Access
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Additional Information
Abstract: Constructing adequate probability models is a basic problem in studies of controlled evolutionary systems. Three approaches are known nowadays to construct models of such systems. There are some disadvantages of the existing approaches and another approach, based on cybernetics, is proposed. Some features of the cybernetic approach are demonstrated in this paper by solving the well-known independence paradox.
References
- M. A. Fedotkin, Nonlocal description of controlled stochastic problems, Mathematical Questions of Cybernetics, issue 7, “Nauka”, Moscow, 1998, pp. 332–344. (Russian)
- M. A. Fedotkin and A. M. Fedotkin, Analysis and optimization of output processes of conflicting Gnedenko-Kovalenko traffic streams under cyclic control, Avtomatika i Telemehanika (2009), no. 12, 92–108; English transl. in Automation and Remote Control (2009), no. 12, 2024–2038.
- A. V. Zorin and M. A. Fedotkin, Optimization of the control of doubly stochastic nonordinary flows in time-sharing systems, Avtomat. i Telemekh. 7 (2005), 102–111 (Russian, with Russian summary); English transl., Autom. Remote Control 66 (2005), no. 7, 1115–1124. MR 2167835, DOI https://doi.org/10.1007/s10513-005-0152-8
- Frederick Mosteller, Fifty challenging problems in probability with solutions, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1965. MR 0397810
- Gábor J. Székely, Paradoxes in probability theory and mathematical statistics, Mathematics and its Applications (East European Series), vol. 15, D. Reidel Publishing Co., Dordrecht, 1986. Translated from the Hungarian by Márta Alpár and Éva Unger. MR 880020
- A. A. Lyapunov and S. V. Yablonskiĭ, Theoretical problems of cybernetics, Problems of Cybernetics, issue 9, “Fizmatgiz”, Moscow, 1963, pp. 5–22. (Russian)
References
- M. A. Fedotkin, Nonlocal description of controlled stochastic problems, Mathematical Questions of Cybernetics, issue 7, “Nauka”, Moscow, 1998, pp. 332–344. (Russian)
- M. A. Fedotkin and A. M. Fedotkin, Analysis and optimization of output processes of conflicting Gnedenko-Kovalenko traffic streams under cyclic control, Avtomatika i Telemehanika (2009), no. 12, 92–108; English transl. in Automation and Remote Control (2009), no. 12, 2024–2038.
- A. V. Zorine and M. A. Fedotkin, Optimization of control of doubly stochastic non-ordinary flows in time-sharing systems, Automation and Remote Control 7 (2005), no. 7, 1115–1124. MR 2167835
- F. Mosteller, Fifty challenging problems in probability with solutions, Addison-Wesley, Reading, MA, 1965. MR 0397810 (53:1666)
- G. Székely, Paradoxes in probability theory and mathematical statistics, Akademiai Kiadó, Budapest, 1986. MR 880020 (88g:60001)
- A. A. Lyapunov and S. V. Yablonskiĭ, Theoretical problems of cybernetics, Problems of Cybernetics, issue 9, “Fizmatgiz”, Moscow, 1963, pp. 5–22. (Russian)
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Additional Information
M. A. Fedotkin
Affiliation:
Department of Applied Probability Theory, Faculty of Computational Mathematics and Cybernetics, N. I. Lobachevsky State University of Nizhni Novgorod, Gagarin Avenue, 23, Nizhni Novgorod, 603950, Russia
Email:
fma5@rambler.ru
Keywords:
Controlled evolutionary systems,
probability model,
cybernetic approach,
independence paradox
Received by editor(s):
June 11, 2011
Published electronically:
January 14, 2013
Additional Notes:
This work was done within the research project “Analysis of discrete managing service systems and systems for calculation of Boole functions”, # 0120.0602598, of N. I. Lobachevsky State University of Nizhni Novgorod
The paper is based on a talk delivered at the International Conference “Modern Stochastics: Theory and Applications II”, held at the Taras Shevchenko Kyiv National University on September 7–11, 2010, and is dedicated to anniversaries of the prominent Ukrainian scientists: Anatoly Skorokhod, Vladimir Korolyuk, and Igor Kovalenko.
Article copyright:
© Copyright 2013
American Mathematical Society
