Corpus ID: 221995470

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

@article{Kuznetsov2020ImplementationOS,
  title={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},
  author={M. D. Kuznetsov and D. Kuznetsov},
  journal={arXiv: Probability},
  year={2020}
}
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 Taylor--Ito and Taylor-Stratonovich expansions and multiple Fourier-Legendre series. Algorithms for the implementation of these methods are constructed and a package of programs on the Python programming language is presented. An important part of… Expand
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
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 ofExpand
New Simple Method of Expansion of Iterated Ito Stochastic integrals of Multiplicity 2 Based on Expansion of the Brownian Motion Using Legendre Polynomials and Trigonometric Functions.
The atricle is devoted to the new simple method for obtainment an expansion of iterated Ito stochastic integrals of multiplicity 2 based on expansion of the Brownian motion (standard Wiener process)Expand
A Comparative Analysis of Efficiency of Using the Legendre Polynomials and Trigonometric Functions for the Numerical Solution of Ito Stochastic Differential Equations
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 differentialExpand
Exact Calculation of the Mean-Square Error in the Method of Approximation of Iterated Ito Stochastic integrals, Based on Generalized Multiple Fourier Series
The article is devoted to the developement of the method of expansion and mean-square approximation of iterated Ito stochastic integrals based on generalized multiple Fourier series converging in theExpand
Expansion of Iterated Stratonovich Stochastic Integrals of Arbitrary Multiplicity Based on Generalized Iterated Fourier Series Converging Pointwise
The article is devoted to the expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity k (k ∈ N) based on generalized iterated Fourier series converging pointwise. The caseExpand
Expansion of Iterated Stratonovich Stochastic Integrals of Fifth Multiplicity, Based on Generalized Multiple Fourier Series
The article is devoted to the construction of expansion of iterated Stratonovich stochastic integrals of fifth multiplicity, based on the method of generalized multiple Fourier series. This expansionExpand
Expansion of Iterated Stratonovich Stochastic Integrals of Multiplicity 2. Combined Approach Based on Generalized Multiple and Iterated Fourier Series
Abstract. The article is devoted to the expansion of iterated Stratonovich stochastic integrals of multiplicity 2 on the base of the combined approach of generalized multiple and repeated FourierExpand
Expansion of Iterated Stratonovich Stochastic Integrals of Multiplicity 3, Based on Generalized Multiple Fourier Series, Converging in the Mean: General Case of Series Summation
The article is devoted to the development of the method of expansion and mean-square approximation of iterated Ito stochastic integrals, based on generalized multiple Fourier series, converging inExpand
Expansions of Iterated Stratonovich Stochastic Integrals of Multiplicities 1 to 4. Combained Approach Based on Generalized Multiple and Repeated Fourier series
The article is devoted to the expansions of iterated Stratonovich stochastic integrals of multiplicities 1 to 4 on the base of the combined approach of generalized multiple and repeated FourierExpand
Expansions of Multiple Stratonovich Stochastic Integrals From the Taylor-Stratonovich Expansion, Based on Multiple Trigonometric Fourier Series. Comparison With the Milstein Expansion
The article is devoted to comparison of the Milstein expansion of multiple stochastic integrals with the method of expansion of multiple stochastic integrals, based on generalized multiple FourierExpand

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