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Sistemy i Sredstva Inform., 2015, Volume 25, Issue 3, Pages 4–23 (Mi ssi414)  

This article is cited in 10 scientific papers (total in 10 papers)

Applications of orthogonal expansions for analytical modeling of multidimensional distributions in stochastic systems on manifold

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: 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.

Keywords: 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).

Funding Agency Grant Number
Russian Foundation for Basic Research 15-07-02244


DOI: https://doi.org/10.14357/08696527150301

Full text: PDF file (275 kB)
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Received: 09.06.2015

Citation: I. N. Sinitsyn, “Applications of orthogonal expansions for analytical modeling of multidimensional distributions in stochastic systems on manifold”, Sistemy i Sredstva Inform., 25:3 (2015), 4–23

Citation in format AMSBIB
\Bibitem{Sin15}
\by I.~N.~Sinitsyn
\paper Applications of orthogonal expansions for analytical modeling of multidimensional distributions in stochastic systems on manifold
\jour Sistemy i Sredstva Inform.
\yr 2015
\vol 25
\issue 3
\pages 4--23
\mathnet{http://mi.mathnet.ru/ssi414}
\crossref{https://doi.org/10.14357/08696527150301}
\elib{https://elibrary.ru/item.asp?id=24347062}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. N. Sinitsyn, “Metody momentov v zadachakh analiticheskogo modelirovaniya raspredelenii v nelineinykh stokhasticheskikh sistemakh na mnogoobraziyakh”, Sistemy i sredstva inform., 25:3 (2015), 24–43  mathnet  crossref  elib
    2. I. N. Sinitsyn, “Analiticheskoe modelirovanie protsessov v dinamicheskikh sistemakh s tsilindricheskimi besselevymi nelineinostyami”, Inform. i ee primen., 9:4 (2015), 37–47  mathnet  crossref  elib
    3. I. N. Sinitsyn, “Ortogonalnye suboptimalnye filtry dlya nelineinykh stokhasticheskikh sistem na mnogoobraziyakh”, Inform. i ee primen., 10:1 (2016), 34–44  mathnet  crossref  elib
    4. I. N. Sinitsyn, V. I. Sinitsyn, “Analiticheskoe modelirovanie raspredelenii v nelineinykh stokhasticheskikh sistemakh na mnogoobraziyakh metodom ellipsoidalnoi approksimatsii”, Inform. i ee primen., 10:1 (2016), 45–55  mathnet  crossref  elib
    5. I. N. Sinitsyn, “Normalnye i ortogonalnye suboptimalnye filtry dlya nelineinykh stokhasticheskikh sistem na mnogoobraziyakh”, Sistemy i sredstva inform., 26:1 (2016), 199–226  mathnet  crossref  elib
    6. I. N. Sinitsyn, V. I. Sinitsyn, I. V. Sergeev, E. R. Korepanov, V. V. Belousov, V. S. Shorgin, “Matematicheskoe obespechenie analiticheskogo modelirovaniya normalnykh protsessov v stokhasticheskikh sistemakh so slozhnymi drobno-ratsionalnymi nelineinostyami”, Sistemy i sredstva inform., 26:1 (2016), 227–247  mathnet  crossref  elib
    7. I. N. Sinitsyn, V. I. Sinitsyn, E. R. Korepanov, “Ellipsoidalnye suboptimalnye filtry dlya nelineinykh stokhasticheskikh sistem na mnogoobraziyakh”, Inform. i ee primen., 10:2 (2016), 24–35  mathnet  crossref  elib
    8. I. N. Sinitsyn, “Parametricheskoe analiticheskoe modelirovanie protsessov v stokhasticheskikh sistemakh, ne razreshennykh otnositelno proizvodnykh”, Sistemy i sredstva inform., 27:1 (2017), 20–45  mathnet  crossref  elib
    9. I. N. Sinitsyn, V. I. Sinitsyn, “Analiticheskoe modelirovanie normalnykh protsessov v volterrovskikh stokhasticheskikh sistemakh”, Sistemy i sredstva inform., 28:2 (2018), 4–19  mathnet  crossref  elib
    10. I. N. Sinitsyn, V. I. Sinitsyn, “Analiticheskoe modelirovanie raspredelenii s invariantnoi meroi v volterrovskikh stokhasticheskikh sistemakh”, Sistemy i sredstva inform., 28:3 (2018), 4–25  mathnet  crossref  elib
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