Expansions of Iterated Stratonovich Stochastic Integrals from the Taylor-Stratonovich Expansion, Based on Multiple Trigonometric Fourier Series. Comparison With the Milstein Expansion

Abstract

The article is devoted to comparison of the Milstein expansion of iterated Stratonovich stochastic integrals with the method of expansion of iterated stochastic integrals based on generalized multiple Fourier series. We consider some practical material connected with the expansions of iterated Stratonovich stochastic integrals from the Taylor-Stratonovich expansion based on multiple trigonometric Fourier series. The comparison of effectiveness of the Fourier-Legendre series as well as the trigonomertic Fourier series for expansion of iterated Stratonovich stochastic integrals is considered.

36 pages. Minor changes in Sect. 3, 4, 7. arXiv admin note: text overlap with arXiv:1712.08991, arXiv:1801.00231, arXiv:1801.03195, arXiv:1801.01564, arXiv:1801.06501, arXiv:1712.09516, arXiv:1801.01962, arXiv:1801.05654, arXiv:1712.09746, arXiv:1801.00784