Systems and Means of Informatics
2017, Volume 27, Issue 4, pp 16-36
ANALYTICAL MODELING OF NORMAL PROCESSES IN STOCHASTIC SYSTEMS WITH INTEGRAL NONLINEARITIES (III)
Abstract
Methodological and algorithmical support for analytical modeling of normal (Gaussian) processes in differential stochastic systems with probabilistic integral nonlinearities (IN) based on Pearson distributions (PD) and stable probabilistic distributions (SPD) is presented. Support is based on the methods of statistical linearization (MSL) and normal approximation (MNA). Probabilistic IN were approximated by power expansions. The MSL and MNA coefficients for probabilistic IN based on PD and SPD are given. The MSL coefficients for incomplete beta-function and F-distribution are considered. Some SPD types are described. Test examples with accuracy estimation are given. Results may be generalized as new types of probabilistic IN (multichannel angular, spherical, etc.) and various numerical approximations (polynomial, rational, fractional rational, orthogonal, asymptotic, and iterative).
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[+] About this article
Title
ANALYTICAL MODELING OF NORMAL PROCESSES IN STOCHASTIC SYSTEMS WITH INTEGRAL NONLINEARITIES (III)
Journal
Systems and Means of Informatics
Volume 27, Issue 4, pp 16-36
Cover Date
2017-10-30
DOI
10.14357/08696527170402
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
analytical modeling; x2-distribution; exponential distribution; gamma-distribution; Hermite polynomial and power expansions; method of normal approximation (MNA); method of statistical linearization (MSL); probabilistic integral nonlinearities (PIN)
Authors
I. N. Sinitsyn 
Author Affiliations
Institute of Informatics Problems, Federal Research Center "Computer Science
and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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