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迭代斯特拉托维奇随机积分的展开方法：基于多重三角傅里叶级数的泰勒-斯特拉托维奇展开，与米尔斯坦展开的比较

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

Peter the Great Saint-Petersburg Polytechnic University（彼得大帝圣彼得堡理工大学）

Dmitriy F. Kuznetsov

备注：
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
发表信息：
Electronic Journal "Differential Equations and Control Processes", no. 4, 2018, pp. A.573-A.581, A.597-A.604 (http://diffjournal.spbu.ru/EN/numbers/2018.4/article.2.1.html)
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AI总结：

本文比较了基于多重三角傅里叶级数的泰勒-斯特拉托维奇展开与米尔斯坦展开在迭代斯特拉托维奇随机积分展开中的有效性。

摘要：

本文致力于比较迭代斯特拉托维奇随机积分的米尔斯坦展开方法与基于广义多重傅里叶级数的展开方法。我们考虑了一些与基于多重三角傅里叶级数的泰勒-斯特拉托维奇展开的迭代斯特拉托维奇随机积分展开相关的实际材料。还讨论了傅里叶-勒杰德系列以及三角傅里叶级数在展开迭代斯特拉托维奇随机积分中的有效性比较。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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