The article is devoted to construction of effective procedures of the mean-square approximation for iterated Stratonovich stochastic integrals of multiplicities 1 to 5. We apply the method of generalized multiple Fourier series for approximation of iterated stochastic integrals. More precisely, we use multiple Fourier-Legendre series converging in the sense of norm in Hilbert space $L_2([t,T]^k),$ $k\in\mathbb{N}.$ Considered iterated Stratonovich stochastic integrals are part of the Taylor-Stratonovich expansion. That is why the results of the article can be applied to implementation of numerical methods with the orders 1.0, 1.5, 2.0 and 2.5 of strong convergence for Ito stochastic differential equations with multidimensional non-commutative noise.
Expansions of Iterated Stratonovich Stochastic Integrals from the Taylor-Stratonovich Expansion, Based on Multiple Trigonometric Fourier Series. Comparison With the Milstein Expansion
Peter the Great Saint-Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
Mean-Square Approximation of Iterated Ito and Stratonovich Stochastic Integrals of Multiplicities 1 to 6 from the Taylor-Ito and Taylor-Stratonovich Expansions Using Legendre Polynomials
Peter the Great Saint-Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
Expansions of Iterated Stratonovich Stochastic Integrals of Multiplicities 1 to 4. Combained Approach Based on Generalized Multiple and Iterated Fourier series
Peter the Great Saint-Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
Expansion of Iterated Stratonovich Stochastic Integrals of Multiplicity 3 Based on Generalized Multiple Fourier Series Converging in the Mean: General Case of Series Summation
Peter the Great Saint-Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
Expansion of Iterated Stratonovich Stochastic Integrals of Fifth, Sixth, Seventh and Eighth Multiplicities Based on Generalized Multiple Fourier Series
Peter the Great Saint-Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
New representations of the Hu-Meyer formulas and series expansion of iterated Stratonovich stochastic integrals with respect to components of a multidimensional Wiener process
Peter the Great Saint-Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
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
Peter the Great Saint-Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
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
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
Explicit One-Step Strong Numerical Methods of Orders 2.0 and 2.5 for Ito Stochastic Differential Equations Based on the Unified Taylor-Ito and Taylor-Stratonovich Expansions
Exact Calculation of the Mean-Square Error in the Method of Expansion of Iterated Ito Stochastic integrals Based on Generalized Multiple Fourier Series
Peter the Great Saint-Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）
Strong Numerical Methods of Orders 2.0, 2.5, and 3.0 for Ito Stochastic Differential Equations Based on the Unified Stochastic Taylor Expansions and Multiple Fourier-Legendre Series
Application of Multiple Fourier-Legendre Series to Implementation of Strong Exponential Milstein and Wagner-Platen Methods for Non-Commutative Semilinear Stochastic Partial Differential Equations
