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
| Autor: | Kuznetsov, Mikhail D., Kuznetsov, Dmitriy F. |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Journal of Physics: Conference Series, Vol. 1925, article id: 012010, 12 pp., 2021 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1742-6596/1925/1/012010 |
| Popis: | 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 $L_2([t, T]^k)$ $(k=1,\ldots,5).$ In this article we use multiple Fourier-Legendre series within the framework of the method of expansion and mean-square approximation of iterated Ito stochastic integrals based on generalized multiple Fourier series. We show that the lengths of sequences of independent standard Gaussian random variables required for the mean-square approximation of iterated Ito stochastic integrals of multiplicities 1 to 5 can be significantly reduced without the loss of the mean-square accuracy of approximation for these stochastic integrals. Comment: 63 pages. Minor changes. arXiv admin note: substantial text overlap with arXiv:2009.14011, arXiv:2003.14184, arXiv:2001.10192, arXiv:1801.03195, arXiv:1901.02345, arXiv:1806.10705, arXiv:1802.00888, arXiv:1801.00231, arXiv:1712.09516, arXiv:1801.01962, arXiv:1712.09746 |
| Databáze: | arXiv |
| Externí odkaz: |
|