Comparative Analysis of the Efficiency of Application of Legendre Polynomials and Trigonometric Functions to the Numerical Integration of Ito Stochastic Differential Equations
| Autor: | Kuznetsov, Dmitriy F. |
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| Rok vydání: | 2018 |
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| Zdroj: | Computational Mathematics and Mathematical Physics, Vol. 59, no. 8, 2019, pp. 1236 -1250 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1134/S0965542519080116 |
| Popis: | The article is devoted to comparative analysis of the efficiency of application of Legendre polynomials and trigonometric functions to the numerical integration of Ito stochastic differential equations in the framework of the method of approximation of iterated Ito and Stratonovich stochastic integrals based on generalized multiple Fourier series. On the example of iterated Ito stochastic integrals of multiplicities 1 to 3, included in the Taylor-Ito expansion, it is shown that expansions of stochastic integrals based on Legendre polynomials are much easier and require significantly less computational costs compared to their analogues obtained using the trigonometric system of functions. The results of the article can be useful for construction of high-order strong numerical methods for Ito stochastic differential equations. Comment: 40 pages. Minor changes. arXiv admin note: substantial text overlap with arXiv:1801.08862, arXiv:1801.00231, arXiv:1807.02190, arXiv:1802.00643, arXiv:1806.10705, arXiv:1712.09516, arXiv:1801.05654, arXiv:1712.08991, arXiv:1801.03195, arXiv:1712.09746, arXiv:1801.01564, arXiv:1801.01962, arXiv:1801.07248 |
| Databáze: | arXiv |
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