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Sistemy i Sredstva Inform., 2015, Volume 25, Issue 2, Pages 3–19 (Mi ssi404)  

This article is cited in 6 scientific papers (total in 6 papers)

Mathematical software for normal processes modeling in stochastic systems with complex irrational nonlinearities

I. N. Sinitsyn, V. I. Sinitsyn, I. V. Sergeev, E.. R. Korepanov, V. V. Belousov, V. S. Shorgin

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

Abstract: Mathematical software for normal stochastic processes (StP) analytical and statistical modeling in differential and difference (discrete) stochastic systems (StS) on manifolds with complex irrational nonlinearities (CIRN) of scalar and vector argument is considered. Typical CIRN and its discrepancy expansions are presented. Equations for the normal approximation method (NAM) and the statistical linearization method (SLM) for normal StP analytical modeling are given. Typical NAM (SLM) integrals and software “StS–CIRN. Analysis” based on cylindrical functions are discussed. Test examples are given.

Keywords: analytical and statistical modeling; complex irrational nonlinearity (CIRN); cylindrical functions; Hermite polynomials; module “StS–CIRN. Analysis”; normal approximation method (NAM); statistical linearization method (SLM).

DOI: https://doi.org/10.14357/08696527150201

Full text: PDF file (255 kB)
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Received: 28.01.2015

Citation: I. N. Sinitsyn, V. I. Sinitsyn, I. V. Sergeev, E.. R. Korepanov, V. V. Belousov, V. S. Shorgin, “Mathematical software for normal processes modeling in stochastic systems with complex irrational nonlinearities”, Sistemy i Sredstva Inform., 25:2 (2015), 3–19

Citation in format AMSBIB
\Bibitem{SinSinSer15}
\by I.~N.~Sinitsyn, V.~I.~Sinitsyn, I.~V.~Sergeev, E..~R.~Korepanov, V.~V.~Belousov, V.~S.~Shorgin
\paper Mathematical software for normal processes modeling in stochastic systems with complex irrational nonlinearities
\jour Sistemy i Sredstva Inform.
\yr 2015
\vol 25
\issue 2
\pages 3--19
\mathnet{http://mi.mathnet.ru/ssi404}
\crossref{https://doi.org/10.14357/08696527150201}
\elib{https://elibrary.ru/item.asp?id=23817342}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. N. Sinitsyn, V. I. Sinitsyn, E. R. Korepanov, “Modelirovanie normalnykh protsessov v stokhasticheskikh sistemakh so slozhnymi transtsendentnymi nelineinostyami”, Inform. i ee primen., 9:2 (2015), 23–29  mathnet  crossref  elib
    2. I. N. Sinitsyn, “Analiticheskoe modelirovanie raspredelenii metodom ortogonalnykh razlozhenii v nelineinykh stokhasticheskikh sistemakh na mnogoobraziyakh”, Inform. i ee primen., 9:3 (2015), 17–24  mathnet  crossref  elib
    3. I. N. Sinitsyn, “Primenenie ortogonalnykh razlozhenii dlya analiticheskogo modelirovaniya mnogomernykh raspredelenii v nelineinykh stokhasticheskikh sistemakh na mnogoobraziyakh”, Sistemy i sredstva inform., 25:3 (2015), 4–23  mathnet  crossref  elib
    4. I. N. Sinitsyn, V. I. Sinitsyn, E. R. Korepanov, “Analiticheskoe modelirovanie normalnykh protsessov v stokhasticheskikh sistemakh so slozhnymi drobno-ratsionalnymi nelineinostyami”, Sistemy i sredstva inform., 25:4 (2015), 4–18  mathnet  crossref  elib
    5. 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
    6. I. N. Sinitsyn, V. I. Sinitsyn, I. V. Sergeev, E. R. Korepanov, V. V. Belousov, V. S. Shorgin, E. S. Agafonov, “Matematicheskoe obespechenie suboptimalnoi normalnoi filtratsii v stokhasticheskikh sistemakh so slozhnymi drobno-ratsionalnymi nelineinostyami”, Sistemy i sredstva inform., 26:3 (2016), 4–25  mathnet  crossref  elib
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