iterated Ito stochastic integral,
iterated Stratonovich stochastic integral,
Ito stochastic differential equation,
multiple Fourier-Legendre series.
Subject:
numerical modeling of stochastic differential equations
Main publications:
Kuznetsov, D. F., Kuznetsov M. D., “Mean-square approximation of iterated stochastic integrals from strong exponential Milstein and Wagner-Platen methods for non-commutative semilinear SPDEs based on multiple Fourier-Legendre series”, Recent Developments in Stochastic Methods and Applications, ICSM-5 2020, Springer Proceedings in Mathematics & Statistics, 371, eds. Shiryaev A.N., Samouylov K.E, Kozyrev D.V., Springer, Cham, 2021, 17–32
Kuznetsov M. D., Kuznetsov, D. F., “SDE–MATH: A software package for the implementation of strong high-order numerical methods for Ito SDEs with multidimensional non-commutative noise based on multiple Fourier–Legendre series”, "Electronic Journal “Differential Equations and Control Processes”", 2021, no. 1, 93-422
Kuznetsov M., Novikova E., Kotenko I., Doynikova E., “Privacy Policies of IoT Devices: Collection and Analysis”, Sensors, 22 (2022), 18-38
Kuznetsov M. D., Novikova E. S., “Krauler dlya formirovaniya dataseta polzovatelskikh soglashenii na ispolzovanie personalnykh dannykh”, Izv. SPbGETU «LETI»., 15:4 (2022), 35-43
4.
Kuznetsov D. F., Kuznetsov M. D., “Optimization of the mean-square approximation procedures
for iterated Stratonovich stochastic integrals of multiplicities
1 to 3 with respect to components of the multi-dimensional
Wiener process based on Multiple Fourier–Legendre series”, MATEC Web of Conferences, 362 (2022), article id: 01014 , 10 pp. PDF
5.
Kuznetsov, D. F., Kuznetsov M. D., “Mean-square approximation of iterated stochastic integrals from strong exponential Milstein and Wagner-Platen methods for non-commutative semilinear SPDEs based on multiple Fourier-Legendre series”, In: Recent Developments in Stochastic Methods and Applications. ICSM-5 2020, Springer Proceedings in Mathematics & Statistics, ISBN 978-3-030-83266-7, 371, eds. Shiryaev A.N., Samouylov K.E, Kozyrev D.V., Springer, Cham, 2021, 17–32Publication Page
6.
Kuznetsov D. F., Kuznetsov M. D., “Optimization of the mean-square approximation procedures for iterated Ito stochastic integrals based on multiple Fourier-Legendre series”, Journal of Physics: Conference Series, 1925 (2021), article id: 012010 , 12 pp. PDF
Mikhail D. Kuznetsov, Dmitriy F. Kuznetsov, “SDE–MATH: A software package for the implementation
of strong high-order numerical methods for Ito SDEs with multidimensional non-commutative noise based on multiple Fourier–Legendre series”, Electronic Journal “Differential Equations and Control Processes”, 2021, no. 1, 93-422Publication PagePDF
8.
Kuznetsov M. D., Myadzel V. S., Novikova E. S., “Primenenie metodov intellektualnogo analiza teksta dlya issledovaniya soglasii na ispolzovanie personalnykh dannykh”, Izv. SPbGETU «LETI»., 2021, no. 4, 42-48
9.
Kuznetsov D.F., Kuznetsov M.D., “A software package for Implementation of strong numerical methods of convergence orders 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 for Ito SDEs with non-commutative multi-dimensional noise”, 19th International Conference “Aviation and Cosmonautics” (AviaSpace-2020). Abstracts (Moscow, MAI, 23-27 November, 2020), Publishing house “Pero”, 2020, 569–570PDF
10.
Kuznetsov M. D., Novikova E. S., “Primenenie latentno-semanticheskogo analiza dlya klasterizatsii skhozhikh po soderzhaniyu tekstov”, Sbornik materialov VIII Mezhdunarodnoi nauchnoi konferentsii «Matematicheskoe i kompyuternoe modelirovanie, Omskii gosudarstvennyi universitet im. F. M. Dostoevskogo, 2020, 125-127PDF
Proceedings
11.
Kuznetsov M. D., “Instrument razmetki dlya polucheniya mnogourovnevoi ierarkhicheskoi vyborki obuchayuschikh dannykh”, Sbornik materialov IX Mezhdunarodnoi nauchnoi konferentsii «Matematicheskoe i kompyuternoe modelirovanie», Omskii gosudarstvennyi universitet im. F. M. Dostoevskogo, 2021, 248-250PDF
ArXiv
12.
Mikhail D. Kuznetsov, Dmitriy F. Kuznetsov, Optimization of the mean-square approximation procedures for iterated Ito stochastic integrals of multiplicities 1 to 5 from the unified Taylor-Ito expansion based on multiple Fourier-Legendre series., 2020 , 63 pp., arXiv: 2010.13564
13.
Mikhail D. Kuznetsov, Dmitriy F. Kuznetsov, Implementation of strong numerical methods of orders 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 for Ito SDEs with non-commutative noise based on the unified Taylor-Ito and Taylor-Stratonovich expansions and multiple Fourier-Legendre series, 2020 , 342 pp., arXiv: 2009.14011
Miscellaneous
14.
Kuznetsov M. D., Kuznetsov D.F., SDE-MATH Fourier-Legendre Coefficients Database, Gosudarstvennaya registratsiya bazy dannykh, okhranyaemoi avtorskimi pravami (RU2021620788), 2021 PDF
15.
Kuznetsov M. D., Kuznetsov D.F., SDE-MATH Software Package, Gosudarstvennaya registratsiya programmy dlya EVM (RU2021616047), 2021 PDF
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