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Inform. Primen., 2013, Volume 7, Issue 2, Pages 4–16 (Mi ia254)  

This article is cited in 32 scientific papers (total in 32 papers)

Parametrical statistical and analytical modeling of distributions in nonlinear stochastic systems on manifolds

I. N. Sinitsyn

IPI RAN

Abstract: Discrete parametrical statistical and analytical modeling methods in nonlinear Ito stochastic systems on manifolds with Wiener and Poisson noises have been developed. For one- and multidimensional densities parametrization, the coefficients in orthogonal expansions of different orders are taken. Special attention is paid to nonlinear correlational theory of statistical and analytical modeling.

Keywords: analytical modeling; method of normal approximation; nonlinear correlational theory; nonlinear Ito stochastic system on manifold; orthogonal expansions method; parametrization of one- and multidimensional densities; statistical linearization method; statistical modeling.

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Citation: I. N. Sinitsyn, “Parametrical statistical and analytical modeling of distributions in nonlinear stochastic systems on manifolds”, Inform. Primen., 7:2 (2013), 4–16

Citation in format AMSBIB
\Bibitem{Sin13}
\by I.~N.~Sinitsyn
\paper Parametrical statistical and analytical modeling of distributions in nonlinear stochastic systems on manifolds
\jour Inform. Primen.
\yr 2013
\vol 7
\issue 2
\pages 4--16
\mathnet{http://mi.mathnet.ru/ia254}


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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, “Analiz i modelirovanie raspredelenii v ereditarnykh stokhasticheskikh sistemakh”, Inform. i ee primen., 8:1 (2014), 2–11  mathnet  crossref  elib
    2. Yu. E. Malashenko, I. A. Nazarova, “Analiz zaderzhek pri dispetcherizatsii odnorodnykh zadanii v usloviyakh neopredelennosti”, Inform. i ee primen., 8:1 (2014), 12–20  mathnet  crossref  elib
    3. I. N. Sinitsyn, “Analiticheskoe modelirovanie raspredelenii s invariantnoi meroi v negaussovskikh differentsialnykh i privodimykh k nim ereditarnykh stokhasticheskikh sistemakh”, Inform. i ee primen., 8:2 (2014), 2–14  mathnet  crossref  elib
    4. I. N. Sinitsyn, I. V. Sergeev, V. I. Sinitsyn, E. R. Korepanov, V. V. Belousov, “Matematicheskoe obespechenie parametricheskogo modelirovaniya raspredelenii v integrodifferentsialnykh stokhasticheskikh sistemakh”, Sistemy i sredstva inform., 24:1 (2014), 4–45  mathnet  crossref  elib
    5. I. N. Sinitsyn, V. I. Sinitsyn, “Analiticheskoe modelirovanie normalnykh protsessov v stokhasticheskikh sistemakh so slozhnymi nelineinostyami”, Inform. i ee primen., 8:3 (2014), 12–18  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 stokhasticheskikh sistem so slozhnymi nelineinostyami”, Sistemy i sredstva inform., 24:3 (2014), 4–17  mathnet  crossref  elib
    7. I. N. Sinitsyn, V. I. Sinitsyn, E. R. Korepanov, “Modelirovanie normalnykh protsessov v stokhasticheskikh sistemakh so slozhnymi irratsionalnymi nelineinostyami”, Inform. i ee primen., 9:1 (2015), 2–8  mathnet  crossref  elib
    8. I. N. Sinitsyn, E. R. Korepanov, “Ustoichivye lineinye uslovno optimalnye filtry i ekstrapolyatory dlya stokhasticheskikh sistem s multiplikativnymi shumami”, Inform. i ee primen., 9:1 (2015), 70–75  mathnet  crossref  elib
    9. 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
    10. 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
    11. I. N. Sinitsyn, I. V. Sergeev, V. I. Sinitsyn, E. R. Korepanov, V. V. Belousov, V. S. Shorgin, “Matematicheskoe obespechenie sinteza diskretnykh filtrov Pugacheva dlya obrabotki normalnykh protsessov v ereditarnykh stokhasticheskikh sistemakh”, Sistemy i sredstva inform., 25:2 (2015), 20–59  mathnet  crossref  elib
    12. 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
    13. I. N. Sinitsyn, E. R. Korepanov, “Normalnye uslovno-optimalnye filtry Pugacheva dlya differentsialnykh stokhasticheskikh sistem, lineinykh otnositelno sostoyaniya”, Inform. i ee primen., 9:2 (2015), 30–38  mathnet  crossref  elib
    14. 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
    15. 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
    16. 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
    17. 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
    18. 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
    19. 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
    20. 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
    21. I. N. Sinitsyn, E. R. Korepanov, “Normalnye filtry Pugacheva dlya avtokorrelirovannykh stokhasticheskikh sistem, lineinykh otnositelno sostoyaniya”, Sistemy i sredstva inform., 26:2 (2016), 63–78  mathnet  crossref  elib
    22. I. N. Sinitsyn, E. R. Korepanov, “Normalnye uslovno-optimalnye filtry i ekstrapolyatory Pugacheva dlya stokhasticheskikh sistem, lineinykh otnositelno sostoyaniya”, Inform. i ee primen., 10:2 (2016), 14–23  mathnet  crossref  elib
    23. I. N. Sinitsyn, “Analiticheskoe modelirovanie normalnykh protsessov v stokhasticheskikh sistemakh so slozhnymi besselevymi nelineinostyami drobnogo poryadka”, Inform. i ee primen., 10:3 (2016), 55–65  mathnet  crossref  elib
    24. I. N. Sinitsyn, E. R. Korepanov, V. V. Belousov, “Simvolnoe analiticheskoe modelirovanie normalnykh protsessov v stokhasticheskikh sistemakh so slozhnymi besselevymi nelineinostyami drobnogo poryadka”, Sistemy i sredstva inform., 26:3 (2016), 26–47  mathnet  crossref  elib
    25. I. N. Sinitsyn, “Analiticheskoe modelirovanie shirokopolosnykh protsessov v stokhasticheskikh sistemakh, ne razreshennykh otnositelno proizvodnykh”, Inform. i ee primen., 11:1 (2017), 3–10  mathnet  crossref  elib
    26. I. N. Sinitsyn, “Analiticheskoe modelirovanie normalnykh protsessov v stokhasticheskikh sistemakh s ellipticheskimi nelineinostyami”, Sistemy i sredstva inform., 27:1 (2017), 3–19  mathnet  crossref  elib
    27. 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
    28. I. N. Sinitsyn, “Analiticheskoe modelirovanie normalnykh protsessov v stokhasticheskikh sistemakh s integralnymi nelineinostyami (I)”, Sistemy i sredstva inform., 27:2 (2017), 3–15  mathnet  crossref  elib
    29. I. N. Sinitsyn, “Analiticheskoe modelirovanie normalnykh protsessov v stokhasticheskikh sistemakh s integralnymi nelineinostyami (II)”, Sistemy i sredstva inform., 27:3 (2017), 23–36  mathnet  crossref  elib
    30. I. N. Sinitsyn, “Analiticheskoe modelirovanie normalnykh protsessov v stokhasticheskikh sistemakh s integralnymi nelineinostyami (III)”, Sistemy i sredstva inform., 27:4 (2017), 16–36  mathnet  crossref  elib
    31. 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
    32. 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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