论文标题
基于广义的多重傅立叶序列的迭代ITO随机积分扩展的方法，具有概率1的收敛证明
The Proof of Convergence with Probability 1 in the Method of Expansion of Iterated Ito Stochastic Integrals Based on Generalized Multiple Fourier Series
论文作者
论文摘要
该文章专门介绍了收敛定理的制定和证明，其概率为1的迭代迭代随机积分的任意多样性的扩展基于普遍的多重傅立叶序列，以希尔伯特空间的规范意义收敛。详细考虑了多个傅里叶 - 法德尔系列和多个三角傅立叶系列的病例。上述定理的证明基于多个傅立叶序列的一般特性，以及基于迭代迭代的随机积分的方法，基于一般的多重傅立叶级数的估计估计。
The article is devoted to the formulation and proof of the theorem on convergence with probability 1 of expansion of iterated Ito stochastic integrals of arbitrary multiplicity based on generalized multiple Fourier series converging in the sense of norm in Hilbert space. The cases of multiple Fourier-Legendre series and multiple trigonomertic Fourier series are considered in detail. The proof of the mentioned theorem is based on the general properties of multiple Fourier series as well as on the estimate for the fourth moment of approximation error in the method of expansion of iterated Ito stochastic integrals based on generalized multiple Fourier series.
