The stability of the Ghurye-Olkin (GO) characterization of Gaussian vectors is analyzed using a partition of the vectors into equivalence classes defined by their matrix factors. The sum of the vectors in each class is near-Gaussian in the characteristic function (c.f.) domain if the GO independence condition is approximately met in the c.f. domain. All vectors have the property that any vector projection is near-Gaussian in the distribution function (d.f.) domain. The proofs of these c.f. and d.f. stabilities use tools that establish the stabilities of theorems by Kac-Bernstein and Cram\'er, respectively. The results are used to prove stability theorems for differential entropies of Gaussian vectors and blind source separation of non-Gaussian sources.

翻译：本文分析利用向量按矩阵因子划分的等价类，对Ghurye-Olkin (GO)高斯向量表征的稳定性进行研究。若在特征函数(c.f.)域中GO独立条件近似满足，则每个等价类内向量之和在该域中近似服从高斯分布。所有向量均具有以下性质：任意向量投影在分布函数(d.f.)域中近似服从高斯分布。上述c.f.域与d.f.域稳定性的证明，分别借助了Kac-Bernstein定理与Cramér定理的稳定性工具。研究结果用于证明高斯向量微分熵的稳定性定理及非高斯源盲源分离的稳定性定理。