Development and application of the Fourier method for the numerical solution of Ito stochastic differential equations

DOI10.1134/S0965542518070096zbMath1483.65016arXiv1712.08991MaRDI QIDQ1991638

D. F. Kuznetsov

Publication date: 30 October 2018

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.08991

zbMATH Keywords

numerical integrationmultiple Fourier seriesLegendre polynomialsIto stochastic differential equationmean square convergenceStratonovich stochastic integralIto stochastic integralrepeated stochastic integralstochastic analog of Taylor's formula

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic integrals (60H05) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (16)

The Proof of Convergence with Probability 1 in the Method of Expansion of Iterated Ito Stochastic Integrals Based on Generalized Multiple Fourier 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 ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A class of new Magnus-type methods for semi-linear non-commutative Itô stochastic differential equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Formulae for Mixed Moments of Wiener Processes and a Stochastic Area Integral ⋮ Explicit one-step numerical method with the strong convergence order of 2.5 for Ito stochastic differential equations with a multi-dimensional nonadditive noise based on the Taylor-Stratonovich expansion ⋮ An analysis of approximation algorithms for iterated stochastic integrals and a Julia and \textsc{Matlab} simulation toolbox ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A comparative analysis of efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations ⋮ Application of the Method of Approximation of Iterated Ito Stochastic Integrals Based on Generalized Multiple Fourier Series to the High-Order Strong Numerical Methods for Non-Commutative Semilinear Stochastic Partial Differential Equations

Cites Work

• Linear stochastic systems with constant coefficients. A statistical approach
• Numerical solution of SDE through computer experiments. Including floppy disk
• New representations of explicit one-step numerical methods for jump-diffusion stochastic differential equations
• The unified Taylor-Itô expansion
• New representations of the Taylor-Stratonovich expansion
• Stratonovich and Ito Stochastic Taylor Expansions
• The approximation of multiple stochastic integrals
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