多重3次迭代Stratonovich随机积分的展开基于收敛于均值的广义多重傅里叶级数：级数求和的一般情况
Expansion of Iterated Stratonovich Stochastic Integrals of Multiplicity 3 Based on Generalized Multiple Fourier Series Converging in the Mean: General Case of Series Summation
AI总结：
本文提出了一种基于广义多重傅里叶级数的迭代Stratonovich随机积分展开方法，并在一般级数求和情况下得出主要结果，适用于Ito随机微分方程的强收敛数值积分。
摘要：
本文致力于开发一种基于收敛于均值的广义多重傅里叶级数的迭代Ito随机积分展开和均方近似方法。我们将该方法适应于从Taylor-Stratonovich展开中得到的三次迭代Stratonovich随机积分。文章的主要结果是利用三重傅里叶-勒让德级数和三重三角傅里叶级数得出的，适用于级数求和的一般情况。一些关于三次到六次迭代Stratonovich随机积分展开的最新结果也被给出。本文的结果可以应用于根据强收敛准则对Ito随机微分方程进行数值积分。
英文摘要：
The article is devoted to the development of the method of expansion and mean-square approximation of iterated Ito stochastic integrals based on generalized multiple Fourier series converging in the mean. We adapt this method for iterated Stratonovich stochastic integrals of multiplicity 3 from the Taylor-Stratonovich expansion. The main result of the article has been derived with using the triple Fourier-Legendre series and triple trigonometric Fourier series for the general case of series summation. Some recent results on the expansion of iterated Stratonovich stochastic integrals of multiplicities 3 to 6 are given. The results of the article can be applied to the numerical integration of Ito stochastic differential equations in accordance with the strong criterion of convergence.
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。
