Corpus ID: 209376690

# Exact Calculation of the Mean-Square Error in the Method of Approximation of Iterated Ito Stochastic integrals, Based on Generalized Multiple Fourier Series

@article{Kuznetsov2018ExactCO,
title={Exact Calculation of the Mean-Square Error in the Method of Approximation of Iterated Ito Stochastic integrals, Based on Generalized Multiple Fourier Series},
author={D. Kuznetsov},
journal={arXiv: Probability},
year={2018}
}
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 the sense of norm in the space $L_2([t, T]^k)$ ($k$ is the multiplicity of the iterated Ito stochastic integral). We obtain the exact and approximate expressions for the mean-square error of approximation of iterated Ito stochastic integrals of multiplicity $k$ ($k\in\mathbb{N}$) from the stochastic… Expand
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#### References

SHOWING 1-10 OF 85 REFERENCES
Application of multiple Fourier-Legendre series to strong exponential Milstein and Wagner- Platen methods for non-commutative semilinear stochastic partial differential equations. [In English
• Differential Equations and Control Processes,
• 2020
Stochastic differential equations: theory and practice of numerical solution. With MATLAB programs, 6th Edition. [In Russian
• Differential Equations and Control Processes,
• 2018
Stochastic Differential Equations: Theory and Practice of Numerical Solution. With MatLab programs, 3rd Edition. [In Russian
• Polytechnical University Publishing House, Saint-Petersburg,
• 2009
Application of multiple Fourier-Legendre series to strong exponential Milstein and Wagner-Platen methods for non-commutative semilinear stochastic partial differential equations
• Differential Equations and Control Processes
• 2020