Systems and Means of Informatics
2017, Volume 27, Issue 2, pp 3-15
ANALYTICAL MODELING OF NORMAL PROCESSES IN STOCHASTIC SYSTEMS WITH INTEGRAL NONLINEARITIES (I)
Abstract
General methodological and algorithmical support for analytical modeling of normal processes in differential stochastic systems (StS) with integral nonlinearities (IN) and Wiener and Poisson noises is presented. Support is based on the methods of normal approximation (MNA) and of statistical linearization (MSL). Integral nonlinearities were approximated by power and Hermite series.
The MSL and MNA coefficients for IN described by Laplace, Fresnel integrals, and sine integrals are given. Necessary information about IN is given and the software tool StS-Analysis.2017 is described. Stochastic dynamic of an integral oscillator is used as a test example. Some generalizations are mentioned.
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[+] About this article
Title
ANALYTICAL MODELING OF NORMAL PROCESSES IN STOCHASTIC SYSTEMS WITH INTEGRAL NONLINEARITIES (I)
Journal
Systems and Means of Informatics
Volume 27, Issue 2, pp 3-15
Cover Date
2017-05-30
DOI
10.14357/08696527170201
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
analytical modeling; Fresnel integral; Hermite polynomial power expansion; integral sine; Laplace function; method of normal approximation (MNA); method of statistical linearization (MSL)
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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