This article is cited in 3 papers

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

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 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.

Keywords: analytical modeling; Fresnel integral; Hermite polynomial power expansion; integral sine; Laplace function; method of normal approximation (MNA); method of statistical linearization (MSL).

Received: 02.03.2017

DOI: 10.14357/08696527170201

Bibliographic databases:

•