Systems and Means of Informatics
2024, Volume 34, Issue 1, pp 4-22
ANALYTICAL MODELING OF STOCHASTIC SYSTEMS WITH RANDOM PARAMETERS AND UNSOLVED DERIVATIVES
Abstract
The paper is devoted to nonlinear correlation methods for analytical modeling in differential stochastic systems with unsolved derivatives (StS USD) and random parameters. Survey is given. Necessary notations concerning integral canonical expansions (ICE) and its linear and nonlinear transforms are presented. It is shown how differential StS USD can be reduced to differential StS. Basic quality analysis algorithms for reducible StS USD are described. Special attention is paid to multicomponent ICE theory of stochastic processes and StS USD reducible to the differential ones. Two types of nonlinear transforms based on linear ICE regression are developed. Normal approximation method is used for ordinary differential equations for conditional probabilistic characteristics: mathematical expectations, covariance matrix, and matrix of covariance functions. For uncondional characteristics, ICE method is implemented. Analytical modeling methods are presented both for stationary and nonstationary regimes. An illustrative example is given. Directions of future generalizations are given.
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[+] About this article
Title
ANALYTICAL MODELING OF STOCHASTIC SYSTEMS WITH RANDOM PARAMETERS AND UNSOLVED DERIVATIVES
Journal
Systems and Means of Informatics
Volume 34, Issue 1, pp 4-22
Cover Date
2024-04-10
DOI
10.14357/08696527240101
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
analytical modeling; integral canonical expansion (ICE); normal approximation method (NAM); stochastic systems with unsolved derivatives (StS USD); conditional and unconditional characteristics
Authors
I. N. Sinitsyn  , 
Author Affiliations
Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Moscow State Aviation Institute (National Research University), 4 Volokolamskoe Shosse, Moscow 125933, Russian Federation
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