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Inform. Primen., 2015, Volume 9, Issue 1, Pages 2–8 (Mi ia352)  

This article is cited in 9 scientific papers (total in 9 papers)

Analytical modeling of normal processes in stochastic systems with complex irrational nonlinearities

I. N. Sinitsyn, V. I. Sinitsyn, E. R. Korepanov

Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of Russian Academy of Sciences

Abstract: Stochastic systems (including manifolds) with Wiener and Poisson noises and complex irrational nonlinearities (CIRN) are considered. Equations and algorithms of analytical modeling based on the normal approximation method (NAM) and the statistical linearization method (SLM) are given. Typical integrals and software based on cylindrical functions for computing deterministic and stochastic CIRN are presented. Seven test examples for typical CIRN are given. Applications to Gibbs distributions and distributions with invariant measure are discussed.

Keywords: analytical and statistical modeling; complex irrational nonlinerarity (CIRN); normal approximation method (NAM); statistical linearization method (SLM); test examples.

DOI: https://doi.org/10.14357/19922264150101

Full text: PDF file (168 kB)
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Received: 15.01.2015

Citation: I. N. Sinitsyn, V. I. Sinitsyn, E. R. Korepanov, “Analytical modeling of normal processes in stochastic systems with complex irrational nonlinearities”, Inform. Primen., 9:1 (2015), 2–8

Citation in format AMSBIB
\Bibitem{SinSinKor15}
\by I.~N.~Sinitsyn, V.~I.~Sinitsyn, E.~R.~Korepanov
\paper Analytical modeling of normal processes in stochastic systems with complex irrational nonlinearities
\jour Inform. Primen.
\yr 2015
\vol 9
\issue 1
\pages 2--8
\mathnet{http://mi.mathnet.ru/ia352}
\crossref{https://doi.org/10.14357/19922264150101}
\elib{https://elibrary.ru/item.asp?id=23575035}


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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, E. R. Korepanov, “Sintez ustoichivykh lineinykh filtrov i ekstrapolyatorov Pugacheva dlya stokhasticheskikh sistem s multiplikativnymi shirokopolosnymi shumami”, Sistemy i sredstva inform., 25:1 (2015), 108–126  mathnet  crossref  elib
    2. I. N. Sinitsyn, V. I. Sinitsyn, I. V. Sergeev, E. R. Korepanov, V. V. Belousov, V. S. Shorgin, “Matematicheskoe obespechenie modelirovaniya normalnykh protsessov v stokhasticheskikh sistemakh so slozhnymi irratsionalnymi nelineinostyami”, Sistemy i sredstva inform., 25:2 (2015), 3–19  mathnet  crossref  elib
    3. 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
    4. 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
    5. 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
    6. 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
    7. V. Yu. Korolev, A. Yu. Korchagin, I. A. Sokolov, “Obobschennye dispersionnye gamma-raspredeleniya kak modeli statisticheskikh zakonomernostei na finansovykh rynkakh”, Inform. i ee primen., 9:4 (2015), 14–28  mathnet  crossref  elib
    8. 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
    9. 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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