| Issue |
MATEC Web of Conferences
Volume 362, 2022
XXII International Conference on Computational Mechanics and Modern Applied Software Systems (CMMASS 2021)
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|
|---|---|---|
| Article Number | 01014 | |
| Number of page(s) | 10 | |
| DOI | https://doi.org/10.1051/matecconf/202236201014 | |
| Published online | 14 September 2022 | |
Optimization of the mean-square approximation procedures for iterated Stratonovich stochastic integrals of multiplicities 1 to 3 with respect to components of the multi-dimensional Wiener process based on Multiple Fourier–Legendre series
1 Institute of Physics and Mechanics, Peter the Great Saint-Petersburg Polytechnic University, 29, Polytechnicheskaya st., 195251, Saint-Petersburg, Russia
2 Faculty of Computer Science and Technologies, Saint-Petersburg Electrotechnical University, 5, Professora Popova st., 197376, Saint-Petersburg, Russia
* e-mail: sde_kuznetsov@inbox.ru
The article is devoted to approximation of iterated Ito and Stratonovich stochastic integrals of multiplicities 1 to 3 by the method of multiple Fourier–Legendre series. The mentioned stochastic integrals are part of strong numerical methods with convergence order 1.5 for Ito stochastic differential equations with multidimensional noncommutative noise. These numerical methods are based on the so-called Taylor–Ito and Taylor–Stratonovich expansions. We calculate the exact lengths of sequences of independent standard Gaussian random variables required for the mean-square approximation of iterated Stratonovich stochastic integrals. Thus, the computational cost for the implementation of numerical methods can be significantly reduced.
© The Authors, published by EDP Sciences, 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/).
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