Informatics and Applications
2016, Volume 10, Issue 1, pp 45-55
ANALYTICAL MODELING OF DISTRIBUTIONS IN STOCHASTIC SYSTEMS ON MANIFOLDS BASED ON ELLIPSOIDAL APPROXIMATION
- I. N. Sinitsyn
- V. I. Sinitsyn
Abstract
Accuracy and sensitivity problems for algorithms of structural analytical modeling of one- and multidimensional distributions based on the method of ellipsoidal approximation (MEA) and the method of ellipsoidal linearization (MEL) are considered. General algorithms of ellipsoidal stochastic analysis in nonlinear stochastic systems on manifolds (MStS) with Wiener and Poisson noises are developed. Special attention is paid to MStS with additive noises. Accuracy and sensitivity equations are presented. For two-dimensional nonlinear circular MStS, accuracy and sensitivity equations are derived. Equations make it possible to calculate probability moments up to the fourth order. Algorithms based on orthogonal expansion of one-dimensional density are compared with algorithms based on MEA (MEL). Some generalizations are given.
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[+] About this article
Title
ANALYTICAL MODELING OF DISTRIBUTIONS IN STOCHASTIC SYSTEMS ON MANIFOLDS BASED ON ELLIPSOIDAL APPROXIMATION
Journal
Informatics and Applications
2016, Volume 10, Issue 1, pp 45-55
Cover Date
2016-01-30
DOI
10.14357/19922264160104
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
accuracy equations; analytical modeling; method of ellipsoidal linearization (MEL); method of ellipsoidal approximation (MEA); sensitivity equations; stochastic system on manifold (MStS)
Authors
I. N. Sinitsyn  and V. I. Sinitsyn
Author Affiliations
Institute of Informatics Problems, Federal Research Center “Computer Sciences and Control” of the Russian
Academy of Sciences, 44-2 Vavilov Str.,Moscow 119333, Russian Federation
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