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Kuznetsov, Dmitriĭ Feliksovich

Author ID: kuznetsov.dmitriy-feliksovich Recent zbMATH articles by "Kuznetsov, Dmitriĭ Feliksovich"
Published as: Kuznetsov, D. F.; Kuznetsov, Dmitriy Feliksovich; Kuznetsov, Dmitriĭ Feliksovich; Kuznetsov, Dmitriy F.
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

Publications by Year

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

Citations by Year