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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
Mikhail D. Kuznetsov, Dmitriy F. Kuznetsov
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 integral…
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
Mikhail D. Kuznetsov, Dmitriy F. Kuznetsov
The article is devoted to the implementation of strong numerical methods with convergence orders and for Ito stochastic differential equati…
The Proof of Convergence with Probability 1 in the Method of Expansion of Iterated Ito Stochastic Integrals Based on Generalized Multiple Fourier Series
Dmitriy F. Kuznetsov
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 bas…
Stochastic Differential Equations: Theory and Practice of Numerical Solution. With Programs on PYTHON and MATLAB
Dmitriy F. Kuznetsov, Mikhail D. Kuznetsov
This monograph is devoted to the problem of numerical integration of stochastic differential equations (SDEs), mainly Ito SDEs. More precisely, the book mainly discusses high-order…
Four New Forms of the Taylor-Ito and Taylor-Stratonovich Expansions and its Application to the High-Order Strong Numerical Methods for Ito Stochastic Differential Equations
Dmitriy F. Kuznetsov
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 t…