Edit Profile (opens in new tab) Kuznetsov, Dmitriĭ Feliksovich Co-Author Distance Author ID: kuznetsov.dmitriy-feliksovich Published as: Kuznetsov, D. F.; Kuznetsov, Dmitriy Feliksovich; Kuznetsov, Dmitriĭ Feliksovich; Kuznetsov, Dmitriy F. more...less Homepage: http://www.sde-kuznetsov.spb.ru External Links: ORCID · arXiv · Google Scholar · ResearchGate · Math-Net.Ru Documents Indexed: 67 Publications since 1997, including 22 Books and 21 Additional arXiv Preprints Co-Authors: 2 Co-Authors with 6 Joint Publications 14 Co-Co-Authors Co-Authors 61 single-authored 3 Kul’chitskiĭ, Oleg Yur’evich 3 Kuznetsov, Mikhail Dmitrievich Serials 22 Differentsial’nye Uravneniya i Protsessy Upravleniya 4 Computational Mathematics and Mathematical Physics 3 Journal of Mathematical Sciences (New York) 2 Automation and Remote Control 1 Ufimskiĭ Matematicheskiĭ Zhurnal all top 5 Fields 44 Probability theory and stochastic processes (60-XX) 30 Numerical analysis (65-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 4 Partial differential equations (35-XX) 1 General and overarching topics; collections (00-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 38 Publications have been cited 248 times in 53 Documents Cited by ▼ Year ▼ Development and application of the Fourier method for the numerical solution of Ito stochastic differential equations. Zbl 1483.65016 Kuznetsov, D. F. 16 2018 A comparative analysis of efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations. Zbl 07139676 Kuznetsov, D. F. 15 2019 On numerical modeling of the multidimensional dynamic systems under random perturbations with the 1.5 and 2.0 orders of strong convergence. Zbl 1400.93285 Kuznetsov, D. F. 15 2018 A method of expansion and approximation of repeated stochastic Stratonovich integrals based on multiple Fourier series on full ortonormal systems. Zbl 07039077 Kuznetsov, D. F. 14 1997 On numerical modeling of the multidimentional dynamic systems under random perturbations with the 2.5 order of strong convergence. Zbl 07097134 Kuznetsov, D. F. 14 2019 Strong approximation of multiple Itô and Stratonovich stochastic integrals: multiple Fourier series approach. 2nd ed. Zbl 1251.60045 Kuznetsov, Dmitriy Feliksovich 12 2011 Multiple Itô and Stratonovich stochastic integrals: approximations, properties, formulas. Zbl 1380.65003 Kuznetsov, Dmitriy Feliksovich 11 2013 New representations of the Taylor-Stratonovich expansion. Zbl 1075.60057 Kuznetsov, D. F. 9 2001 Stochastic differential equations: theory and practice of numerical solution. 2nd ed. (Стохастические дифференциальные уравнения: теория и практика численного решения.) Zbl 1206.60001 Kuznetsov, D. F. 8 2007 Multiple Itô and Stratonovich stochastic integrals: Fourier-Legendre and trigonometric expansions, approximations, formulas. Zbl 1373.60001 Kuznetsov, Dmitriy F. 8 2017 Strong approximation of iterated Ito and Stratonovich stochastic integrals based on generalized multiple Fourier series. Application to numerical solution of Ito SDEs and semilinear SPDEs. Zbl 1456.65001 Kuznetsov, Dmitriy Feliksovich 8 2020 Stochastic differential equations: theory and practice of numerical solution. 4th ed. (Стохастические дифференциальные уравнения: теория и практика численного решения.) Zbl 1206.60003 Kuznetsov, D. F. 7 2010 Application of the method of approximation of iterated stochastic Itô integrals based on generalized multiple Fourier series to the high-order strong numerical methods for non-commutative semilinear stochastic partial differential equations. Zbl 1433.60077 Kuznetsov, Dmitriĭ Feliksovich 7 2019 Explicit one-step numerical method with the strong convergence order of 2.5 for Ito stochastic differential equations with a multi-dimensional nonadditive noise based on the Taylor-Stratonovich expansion. Zbl 1469.65032 Kuznetsov, D. F. 7 2020 The proof of convergence with probability 1 in the method of expansion of iterated Ito stochastic integrals based on generalized multiple Fourier series. Zbl 1457.60082 Kuznetsov, Dmitriĭ Feliksovich 7 2020 Approximation of iterated Ito stochastic integrals of the second multiplicity based on the Wiener process expansion using Legendre polynomials and trigonometric functions. Zbl 07189588 Kuznetsov, Dmitriĭ Feliksovich 7 2019 Expansion of multiple Stratonovich stochastic integrals of second multiplicity, based on double Fourier-Legendre series summarized by Prinsheim method. Zbl 1391.60124 Kuznetsov, Dmitriĭ Feliksovich 7 2018 Stochastic differential equations: theory and practice of numerical solution. 3rd ed. (Стохастические дифференциальные уравнения: теория и практика численного решения.) Zbl 1206.60002 Kuznetsov, D. F. 6 2009 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. Zbl 1468.65241 Kuznetsov, Mikhail Dmitrievich; Kuznetsov, Dmitriy Feliksovich 6 2021 Application of multiple Fourier-Legendre series to implementation of strong exponential Milstein and Wagner-Platen methods for non-commutative semilinear stochastic partial differential equations. Zbl 1476.60109 Kuznetsov, Dmitriy Feliksovich 6 2020 Numerical integration of stochastic differential equations. 2. (Численное интегрирование стохастических дифференциальных уравнений. 2.) Zbl 1378.65004 Kuznetsov, Dmitriy Feliksovich 5 2006 New representations of explicit one-step numerical methods for jump-diffusion stochastic differential equations. Zbl 1025.60033 Kuznetsov, D. F. 5 2001 Expansion of iterated Stratonovich stochastic integrals based on generalized multiple Fourier series. Zbl 1463.60076 Kuznetsov, Dmitriĭ Feliksovich 5 2019 Stochastic differential equations: theory and practice of numerical solution. With Matlab programs. 6th revised and expanded edition. (Стохастические дифференциальные уравнения: теория и практика численного решения. С программами в среде Matlab.) Zbl 1404.60002 Kuznetsov, Dmitriy Feliksovich 5 2018 Numerical modeling of stochastic differential equations and stochastic integrals. (Chislennoe modelirovanie stokhasticheskikh differentsial’nykh uravnenij i stokhasticheskikh integralov.) Zbl 0935.65003 Kuznetsov, D. F. 4 1999 Mean-square approximation of iterated Ito and Stratonovich stochastic integrals: method of generalized multiple Fourier series. Application to numerical integration of Ito SDEs and semilinear SPDEs. Zbl 1492.60004 Kuznetsov, Dmitriy Feliksovich 4 2021 Approximation of multiple Itô and Stratonovich stochastic integrals. Multiple Fourier series approach. Revised ed. Zbl 1255.60085 Kuznetsov, Dmitriy Feliksovich 4 2012 Some questions in the numerical solution of Itô stochastic differential equations. (Nekotorye voprosy teorii chislennogo resheniya stokhasticheskikh differentsial’nykh uravnenij Ito.) Zbl 0908.60054 Kuznetsov, D. F. 3 1998 Expansion of the Stratonovich multiple stochastic integrals based on the Fourier multiple series. Zbl 1001.60063 Kuznetsov, D. F. 3 1999 Stochastic differential equations: theory and practice of numerical solution. (Стохастические дифференциальные уравнения: теория и практика численного решения.) Zbl 1378.60008 Kuznetsov, Dmitriy Feliksovich 3 2007 Multiple stochastic Itô and Stratonovich integrals and multiple Fourier series. (Повторные стохастические интегралы Ито и стратоновича и кратные ряды фурье.) Zbl 1476.60001 Kuznetsov, D. F. 3 2010 Unified Taylor-Itô expansion. Zbl 1506.60056 Kul’chitskiĭ, O. Yu.; Kuznetsov, D. F. 3 1997 A new approach to the series expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity with respect to components of the multidimensional Wiener process. Zbl 1502.60087 Kuznetsov, Dmitriĭ Feliksovich 3 2022 Stochastic differential equations: theory and practice of numerical solution. With Matlab programs. 5th edition. (Стохастические дифференциальные уравнения: теория и практика численного решения. С программами в среде Matlab.) Zbl 1368.60004 Kuznetsov, Dmitriy Feliksovich 2 2017 Problems of the numerical analysis of Itô stochastic differential equations. (Некоторые вопросы теории численного решения стохастических дифференциальных уравнений Ито.) Zbl 1522.65004 Kuznetsov, D. F. 2 1998 A new approach to the series expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity with respect to components of the multidimensional Wiener process. II. Zbl 1503.60063 Kuznetsov, Dmitriy Feliksovich 2 2022 Numerical integration of stochastic differential equations. (Численное интегрирование стохастических дифференциальных уравнений.) Zbl 1378.65005 Kuznetsov, Dmitriy Feliksovich 1 2001 Numerical simulation of stochastic systems of linear stationary differential equations. Zbl 07039051 Kul’chitskiĭ, O. Yu.; Kuznetsov, D. F. 1 1998 A new approach to the series expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity with respect to components of the multidimensional Wiener process. Zbl 1502.60087 Kuznetsov, Dmitriĭ Feliksovich 3 2022 A new approach to the series expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity with respect to components of the multidimensional Wiener process. II. Zbl 1503.60063 Kuznetsov, Dmitriy Feliksovich 2 2022 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. Zbl 1468.65241 Kuznetsov, Mikhail Dmitrievich; Kuznetsov, Dmitriy Feliksovich 6 2021 Mean-square approximation of iterated Ito and Stratonovich stochastic integrals: method of generalized multiple Fourier series. Application to numerical integration of Ito SDEs and semilinear SPDEs. Zbl 1492.60004 Kuznetsov, Dmitriy Feliksovich 4 2021 Strong approximation of iterated Ito and Stratonovich stochastic integrals based on generalized multiple Fourier series. Application to numerical solution of Ito SDEs and semilinear SPDEs. Zbl 1456.65001 Kuznetsov, Dmitriy Feliksovich 8 2020 Explicit one-step numerical method with the strong convergence order of 2.5 for Ito stochastic differential equations with a multi-dimensional nonadditive noise based on the Taylor-Stratonovich expansion. Zbl 1469.65032 Kuznetsov, D. F. 7 2020 The proof of convergence with probability 1 in the method of expansion of iterated Ito stochastic integrals based on generalized multiple Fourier series. Zbl 1457.60082 Kuznetsov, Dmitriĭ Feliksovich 7 2020 Application of multiple Fourier-Legendre series to implementation of strong exponential Milstein and Wagner-Platen methods for non-commutative semilinear stochastic partial differential equations. Zbl 1476.60109 Kuznetsov, Dmitriy Feliksovich 6 2020 A comparative analysis of efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations. Zbl 07139676 Kuznetsov, D. F. 15 2019 On numerical modeling of the multidimentional dynamic systems under random perturbations with the 2.5 order of strong convergence. Zbl 07097134 Kuznetsov, D. F. 14 2019 Application of the method of approximation of iterated stochastic Itô integrals based on generalized multiple Fourier series to the high-order strong numerical methods for non-commutative semilinear stochastic partial differential equations. Zbl 1433.60077 Kuznetsov, Dmitriĭ Feliksovich 7 2019 Approximation of iterated Ito stochastic integrals of the second multiplicity based on the Wiener process expansion using Legendre polynomials and trigonometric functions. Zbl 07189588 Kuznetsov, Dmitriĭ Feliksovich 7 2019 Expansion of iterated Stratonovich stochastic integrals based on generalized multiple Fourier series. Zbl 1463.60076 Kuznetsov, Dmitriĭ Feliksovich 5 2019 Development and application of the Fourier method for the numerical solution of Ito stochastic differential equations. Zbl 1483.65016 Kuznetsov, D. F. 16 2018 On numerical modeling of the multidimensional dynamic systems under random perturbations with the 1.5 and 2.0 orders of strong convergence. Zbl 1400.93285 Kuznetsov, D. F. 15 2018 Expansion of multiple Stratonovich stochastic integrals of second multiplicity, based on double Fourier-Legendre series summarized by Prinsheim method. Zbl 1391.60124 Kuznetsov, Dmitriĭ Feliksovich 7 2018 Stochastic differential equations: theory and practice of numerical solution. With Matlab programs. 6th revised and expanded edition. (Стохастические дифференциальные уравнения: теория и практика численного решения. С программами в среде Matlab.) Zbl 1404.60002 Kuznetsov, Dmitriy Feliksovich 5 2018 Multiple Itô and Stratonovich stochastic integrals: Fourier-Legendre and trigonometric expansions, approximations, formulas. Zbl 1373.60001 Kuznetsov, Dmitriy F. 8 2017 Stochastic differential equations: theory and practice of numerical solution. With Matlab programs. 5th edition. (Стохастические дифференциальные уравнения: теория и практика численного решения. С программами в среде Matlab.) Zbl 1368.60004 Kuznetsov, Dmitriy Feliksovich 2 2017 Multiple Itô and Stratonovich stochastic integrals: approximations, properties, formulas. Zbl 1380.65003 Kuznetsov, Dmitriy Feliksovich 11 2013 Approximation of multiple Itô and Stratonovich stochastic integrals. Multiple Fourier series approach. Revised ed. Zbl 1255.60085 Kuznetsov, Dmitriy Feliksovich 4 2012 Strong approximation of multiple Itô and Stratonovich stochastic integrals: multiple Fourier series approach. 2nd ed. Zbl 1251.60045 Kuznetsov, Dmitriy Feliksovich 12 2011 Stochastic differential equations: theory and practice of numerical solution. 4th ed. (Стохастические дифференциальные уравнения: теория и практика численного решения.) Zbl 1206.60003 Kuznetsov, D. F. 7 2010 Multiple stochastic Itô and Stratonovich integrals and multiple Fourier series. (Повторные стохастические интегралы Ито и стратоновича и кратные ряды фурье.) Zbl 1476.60001 Kuznetsov, D. F. 3 2010 Stochastic differential equations: theory and practice of numerical solution. 3rd ed. (Стохастические дифференциальные уравнения: теория и практика численного решения.) Zbl 1206.60002 Kuznetsov, D. F. 6 2009 Stochastic differential equations: theory and practice of numerical solution. 2nd ed. (Стохастические дифференциальные уравнения: теория и практика численного решения.) Zbl 1206.60001 Kuznetsov, D. F. 8 2007 Stochastic differential equations: theory and practice of numerical solution. (Стохастические дифференциальные уравнения: теория и практика численного решения.) Zbl 1378.60008 Kuznetsov, Dmitriy Feliksovich 3 2007 Numerical integration of stochastic differential equations. 2. (Численное интегрирование стохастических дифференциальных уравнений. 2.) Zbl 1378.65004 Kuznetsov, Dmitriy Feliksovich 5 2006 New representations of the Taylor-Stratonovich expansion. Zbl 1075.60057 Kuznetsov, D. F. 9 2001 New representations of explicit one-step numerical methods for jump-diffusion stochastic differential equations. Zbl 1025.60033 Kuznetsov, D. F. 5 2001 Numerical integration of stochastic differential equations. (Численное интегрирование стохастических дифференциальных уравнений.) Zbl 1378.65005 Kuznetsov, Dmitriy Feliksovich 1 2001 Numerical modeling of stochastic differential equations and stochastic integrals. (Chislennoe modelirovanie stokhasticheskikh differentsial’nykh uravnenij i stokhasticheskikh integralov.) Zbl 0935.65003 Kuznetsov, D. F. 4 1999 Expansion of the Stratonovich multiple stochastic integrals based on the Fourier multiple series. Zbl 1001.60063 Kuznetsov, D. F. 3 1999 Some questions in the numerical solution of Itô stochastic differential equations. (Nekotorye voprosy teorii chislennogo resheniya stokhasticheskikh differentsial’nykh uravnenij Ito.) Zbl 0908.60054 Kuznetsov, D. F. 3 1998 Problems of the numerical analysis of Itô stochastic differential equations. (Некоторые вопросы теории численного решения стохастических дифференциальных уравнений Ито.) Zbl 1522.65004 Kuznetsov, D. F. 2 1998 Numerical simulation of stochastic systems of linear stationary differential equations. Zbl 07039051 Kul’chitskiĭ, O. Yu.; Kuznetsov, D. F. 1 1998 A method of expansion and approximation of repeated stochastic Stratonovich integrals based on multiple Fourier series on full ortonormal systems. Zbl 07039077 Kuznetsov, D. F. 14 1997 Unified Taylor-Itô expansion. Zbl 1506.60056 Kul’chitskiĭ, O. Yu.; Kuznetsov, D. F. 3 1997 all cited Publications top 5 cited Publications all top 5 Cited by 56 Authors 18 Kuznetsov, Dmitriĭ Feliksovich 13 Rybakov, Konstantin Aleksandrovich 3 Averina, Tat’yana Aleksandrovna 2 Burrage, Kevin 2 Karachanskaya (Chalykh), Elena V. 2 Komori, Yoshio 2 Yang, Guoguo 1 Aksenova, V. Yu 1 Alipanah, Amjad 1 Arkhipov, N. S. 1 Asylgareev, Artur Salavatovich 1 Bardina, Xavier 1 Burrage, Pamela M. 1 Chernogorsky, S. 1 Chernykh, N. V. 1 Chichvarin, A. V. 1 Ding, Xiaohua 1 Druzhinina, O. V. 1 Duffaut Espinosa, Luis A. 1 Egorov, Aleksandr Dmitrievich 1 Ermakov, Sergeĭ Mikhaĭlovich 1 Gaponenko, E. V. 1 González, Oscar R. 1 Gray, W. Steven 1 Habermann, Karen 1 Kallemov, Bakytzhan 1 Kastner, Felix 1 Kudryavtseva, I. A. 1 Kuznetsov, Mikhail Dmitrievich 1 Malyutin, Viktor Borisovich 1 Marchenko, I. G. 1 Marchenko, Ivan Ivanovich 1 Masina, O. N. 1 Miller, Gregory Hale 1 Mishura, Yuliya Stepanivna 1 Misyurin, Sergeĭ Yur’evich 1 Osintsev, M. S. 1 Pakshin, P. V. 1 Panteleev, Andreĭ Vladimirovich 1 Pogosian, Anna A. 1 Polyanskiĭ, Ivan Sergeevich 1 Rößler, Andreas 1 Rovira, Carles 1 Rybak, L. A. 1 Saraev, Aleksandr Leonidovich 1 Saraev, Leonid Aleksandrovich 1 Schurz, Henri 1 Shariati, Nasim Madah 1 Shvaĭ, O. V. 1 Shvetsov, Konstantin 1 Sobolev, Vladimir A. 1 Trebotich, David P. 1 Yaghouti, Mohammadreza 1 Zav’yalova, Tat’yana Viktorovna 1 Zherelo, Anatoly V. 1 Zhiglo, A. V. all top 5 Cited in 22 Serials 21 Differentsial’nye Uravneniya i Protsessy Upravleniya 6 Automation and Remote Control 3 Computational Mathematics and Mathematical Physics 2 Numerical Algorithms 2 Journal of Computer and Systems Sciences International 2 Monte Carlo Methods and Applications 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Molecular Simulation 1 Programming and Computer Software 1 SIAM Journal on Numerical Analysis 1 Publicacions Matemàtiques 1 Journal of Statistical Computation and Simulation 1 Theory of Probability and Mathematical Statistics 1 Combinatorics, Probability and Computing 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Sibirskiĭ Zhurnal Vychislitel’noĭ Matematiki 1 Matematicheskie Trudy 1 Stochastics 1 Journal of Physics A: Mathematical and Theoretical 1 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 1 Nonlinear Phenomena in Complex Systems (Minsk) 1 Ufimskiĭ Matematicheskiĭ Zhurnal all top 5 Cited in 16 Fields 40 Probability theory and stochastic processes (60-XX) 25 Numerical analysis (65-XX) 12 Systems theory; control (93-XX) 4 Partial differential equations (35-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 2 Approximations and expansions (41-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Operations research, mathematical programming (90-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Number theory (11-XX) 1 Ordinary differential equations (34-XX) 1 Operator theory (47-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year