# 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

@article{Kuznetsov2020OptimizationOT,
title={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},
author={M. D. Kuznetsov and D. Kuznetsov},
journal={arXiv: Probability},
year={2020}
}
• Published 2020
• Mathematics
• arXiv: Probability
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, 1.5, 2.0, and 2.5 for Ito stochastic differential equations with multidimensional non-commutative noise based on the unified Taylor-Ito expansion and multiple Fourier-Legendre series converging in the sense of norm in Hilbert space $L_2([t, T]^k)$ $(k… Expand 7 Citations 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 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 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 Abstract. The article is devoted to the construction of explicit one-step strong numerical methods with the orders of convergence 2.0, 2,5, and 3.0 for Ito stochastic differential equations withExpand #### References SHOWING 1-10 OF 76 REFERENCES Problems of the numerical analysis of Ito stochastic differential equations. [In Russian]. Electronic Journal ”Differential Equations and Control Processes • ISSN 1817-2172 (online), • 1998 Stochastic Differential Equations: Theory and Practice of Numerical Solution. With MATLAB Programs, 6th Edition. [In Russian]. Electronic Journal ”Differential Equations and Control Processes • 2018 Stochastic Differential Equations: Theory and Practice of Numerical Solution. With Programs on MATLAB, 5th Edition. [In Russian]. Electronic Journal ”Differential Equations and Control Processes • 2017 Numerical Solution Of Sde Through Computer Experiments This numerical solution of sde helps people to enjoy a good book with a cup of coffee in the afternoon, instead they juggled with some malicious bugs inside their computer. Expand Numerical Solution of Stochastic Differential Equations This paper provides an introduction to the main concepts and techniques necessary for someone who wishes to carryout numerical experiments involving Stochastic Differential Equation (SDEs). As SDEsExpand Multidimensional Milstein scheme for solving a stochastic model for prebiotic evolution Abstract A multi-dimensional system of stochastic differential equations is presented for modeling prebiotic evolution. The system consists of replication of several reacting species using activatedExpand Multiple stochastic Ito and Stratonovich integrals and multiple Fourier serieses. [In Russian]. Electronic Journal ”Differential Equations and Control Processes • ISSN 1817-2172 (online), • 2010 Numerical Integration of Stochastic Differential Equations This chapter provides an introduction into the numerical integration of stochastic differential equations (SDEs). Again X t denotes a stochastic process and solution of an SDE,$\$\frac{{\partialExpand
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• Mathematics
• 1992
A method for approximating the multiple stochastic integrals appearing in stochaslic Taylor expansions is proposed. It is based on a series expansion of the Brownian bridge process. Some higher orderExpand
Numerical integration of stochastic differential equations
A procedure for numerical integration of a stochastic differential equation, by extension of the Runge-Kutta method, is presented. The technique produces results which are statistically correct to aExpand