Zobrazeno 1 - 10
of 282
pro vyhledávání: '"Kuznetsov, Dmitriy A."'
Autor:
Kuznetsov, Dmitriy F.
Publikováno v:
Electronic Journal Differential Equations and Control Processes, 2023, no. 4, 67-124
The article is devoted to a new proof of the expansion for iterated Ito stochastic integrals with respect to the components of a multidimensional Wiener process. The above expansion is based on Hermite polynomials and generalized multiple Fourier ser
Externí odkaz:
http://arxiv.org/abs/2307.11006
Publikováno v:
Journal of Physics: Conference Series, Vol. 1925, article id: 012010, 12 pp., 2021
The article is devoted to optimization of the mean-square approximation procedures for iterated Ito stochastic integrals of multiplicities 1 to 5. The mentioned stochastic integrals are part of strong numerical methods with convergence orders 1.0, 1.
Externí odkaz:
http://arxiv.org/abs/2010.13564
Publikováno v:
Electronic Journal Differential Equations and Control Processes, no. 1, 2021, pp. 93-422 (https://diffjournal.spbu.ru/EN/numbers/2021.1/article.1.5.html)
The article is devoted to the implementation of strong numerical methods with convergence orders $0.5,$ $1.0,$ $1.5,$ $2.0,$ $2.5,$ and $3.0$ for Ito stochastic differential equations with multidimensional non-commutative noise based on the unified T
Externí odkaz:
http://arxiv.org/abs/2009.14011
Autor:
Kuznetsov, Dmitriy F.
Publikováno v:
Electronic Journal "Differential Equations and Control Processes", no. 2, 2020, pp. 89-117. Available at: https://diffjournal.spbu.ru/EN/numbers/2020.2/article.1.6.html
The article is devoted to the formulation and proof of the theorem on convergence with probability 1 of expansion of iterated Ito stochastic integrals of arbitrary multiplicity based on generalized multiple Fourier series converging in the sense of n
Externí odkaz:
http://arxiv.org/abs/2006.16040
Autor:
Kuznetsov, Dmitriy F.
Publikováno v:
Electronic Journal Differential Equations and Control Processes, no. 1, 2023, pp. A.1-A.947 (https://diffjournal.spbu.ru/EN/numbers/2023.1/article.1.10.html)
The book is devoted to the strong approximation of iterated stochastic integrals (ISIs) in the context of numerical integration of Ito SDEs and non-commutative semilinear SPDEs with nonlinear multiplicative trace class noise. The monograph opens up a
Externí odkaz:
http://arxiv.org/abs/2003.14184
Autor:
Kuznetsov, Dmitriy F.
Publikováno v:
Electronic Journal Differential Equations and Control Processes, no. 4, 2018, pp. A.184 - A.229, A.241 - A.248 (http://diffjournal.spbu.ru/EN/numbers/2018.4/article.2.1.html)
The problem of the Taylor-Ito and Taylor-Stratonovich expansions of the Ito stochastic processes in a neighborhood of a fixed moment of time is considered. The classical forms of the Taylor-Ito and Taylor-Stratonovich expansions are transformed to th
Externí odkaz:
http://arxiv.org/abs/2001.10192
Autor:
Kuznetsov, Dmitriy F.
Publikováno v:
Electronic Journal Differential Equations and Control Processes, no. 3, 2020, pp. 129-162 (https://diffjournal.spbu.ru/RU/numbers/2020.3/article.1.6.html)
The article is devoted to the application of multiple Fourier-Legendre series to implementation of strong exponential Milstein and Wagner-Platen methods for non-commutative semilinear stochastic partial differential equations with multiplicative trac
Externí odkaz:
http://arxiv.org/abs/1912.02612
Publikováno v:
In Journal of Photochemistry & Photobiology, A: Chemistry 1 October 2023 444
Autor:
Kuznetsov, Dmitriy F.
Publikováno v:
Electronic Journal Differential Equations and Control Processes, no. 3, 2019, pp. 18 - 62 (http://diffjournal.spbu.ru/EN/numbers/2019.3/article.1.2.html)
We consider a method for the approximation of iterated stochastic integrals of arbitrary multiplicity $k$ $(k\in \mathbb{N})$ with respect to the infinite-dimensional $Q$-Wiener process using the mean-square approximation method of iterated Ito stoch
Externí odkaz:
http://arxiv.org/abs/1905.03724
Autor:
Kuznetsov, Dmitriy F.
Publikováno v:
Computational Mathematics and Mathematical Physics, Vol. 59, no. 8, 2019, pp. 1236 -1250
The article is devoted to comparative analysis of the efficiency of application of Legendre polynomials and trigonometric functions to the numerical integration of Ito stochastic differential equations in the framework of the method of approximation
Externí odkaz:
http://arxiv.org/abs/1901.02345