Systems and Means of Informatics
2015, Volume 25, Issue 3, pp 4-23APPLICATIONS OF ORTHOGONAL EXPANSIONS FOR ANALYTICAL MODELING OF MULTIDIMENSIONAL DISTRIBUTIONS IN STOCHASTIC SYSTEMS ON MANIFOLD
- I. N. Sinitsyn
Abstract
Problems of accuracy and sensitivity estimation for algorithms of the analytical modeling method (AMM) based on the multidimensional orthogonal expansions method (OEM) and quasi-moments (QMM) in stochastic systems on manifolds (MStS) with Wiener and Poisson noises are considered. Equations for multidimensional OEM and QMM are given. Problems of reduction of the number of equations for OEM and QMM are discussed. For typical reliability and security problems, equations for OEM and QMM sensitivity functions of the first order are deduced. The results are the basis of the symbolic software tools in MATLAB-MAPLE. A test example for scalar stochastic systems with cybic nonlinearity and multiplicative Gaussian noise is given. Some generalizations are presented.[+] References (20)
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[+] About this article
Title
APPLICATIONS OF ORTHOGONAL EXPANSIONS FOR ANALYTICAL MODELING OF MULTIDIMENSIONAL DISTRIBUTIONS IN STOCHASTIC SYSTEMS ON MANIFOLDJournal
Systems and Means of InformaticsVolume 25, Issue 3, pp 4-23
Cover Date
2015-09-30DOI
10.14357/08696527150301Print ISSN
0869-6527Publisher
Institute of Informatics Problems, Russian Academy of SciencesAdditional Links
Key words
accuracy equations; analytical modeling method (AMM); one- and multidimensional density expansions; orthogonal expansions method (OEM); quasi-moments method (QMM); sensitivity equations; stochastic system on manifold (MStS)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