In this study, some new results on convergence properties for -coordinatewise negatively associated random vectors in Hilbert space are investigated. The weak law of large numbers, strong law of large numbers, complete convergence, and complete moment convergence for linear process of H-valued -coordinatewise negatively associated random vectors with random coefficients are established. These results improve and generalise some corresponding ones in the literature.

中文翻译：

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希尔伯特空间中坐标负相关随机向量的收敛定理

在这项研究中，研究了希尔伯特空间中-坐标负相关随机向量的收敛特性的一些新结果。建立了具有随机系数的H值-坐标负相关随机向量的线性过程的弱大数定律、强大数定律、完全收敛和完全矩收敛。这些结果改进和概括了文献中的一些相应结果。