This article is cited in 2 papers

Analytical modeling of normal processes in stochastic systems with integral nonlinearities (II)

I. N. Sinitsyn

Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow, 119333, Russian Federation

Abstract: General methodological and algorithmical support for analytical modeling of normal processes in differential stochastic systems (StS) with probabilistic integral nonlinearities (PIN) and Wiener and Poisson noises is presented. The support is based on the method of normal approximation (MNA) and the method of statistical linearization (MSL). Probabilistic integral nonlinearities were approximated by power and Hermite series. The MSL and MNA coefficients for PIN described by exponential, gamma, and $\chi^2$-distributions are presented. The necessary information about the function of the parabolic cylinder is also presented. Two test examples are considered. Some generalizations are mentioned.

Keywords: analytical modeling; $\chi^2$-distribution; exponential distribution; gamma-distribution; Hermite polynomial and power expansion; method of normal approximation (MNA); method of statistical linearization (MSL); probabilistic integral nonlinearities (PIN).

Received: 23.03.2017

DOI: 10.14357/08696527170303

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