A comparative analysis of efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations

DOI10.1134/S0965542519080116MaRDI QIDQ2278208

D. F. Kuznetsov

Publication date: 4 December 2019

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

Full work available at URL: https://arxiv.org/abs/1901.02345

zbMATH Keywords

numerical integrationmultiple Fourier seriesLegendre polynomialsIto stochastic differential equationmultiple stochastic integralmean square convergenceStratonovich stochastic integralIto-Taylor expansionIto stochastic integral

Mathematics Subject Classification ID

Numerical analysis (65-XX) Probability theory and stochastic processes (60-XX)

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 ⋮ Unnamed Item ⋮ A class of new Magnus-type methods for semi-linear non-commutative Itô stochastic differential equations ⋮ Unnamed Item ⋮ A convergent wavelet-based method for solving linear stochastic differential equations included 1D and 2D noise ⋮ Unnamed Item ⋮ Formulae for Mixed Moments of Wiener Processes and a Stochastic Area Integral ⋮ 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 ⋮ 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

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• On numerical modeling of the multidimentional dynamic systems under random perturbations with the 2.5 order of strong convergence
• Stratonovich and Ito Stochastic Taylor Expansions
• The approximation of multiple stochastic integrals
• Random Ordinary Differential Equations and Their Numerical Solution
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