论文标题
$ \ mathbf {g} $ - 中央限制定理和$ \ mathbf {g} $ - 关联随机变量的不变性原理
$\mathbf{G}$-Central limit theorems and $\mathbf{G}$-invariance principles for associated random variables
论文作者
论文摘要
对关联数据的研究渐近限制主要集中于相关数据汇总和相关不变性原则的限制定理。在一系列论文中，我们将通过考虑任意无限分解（可划分的）限制定律来设定理论的一般框架，并研究相关的功能定律融合到Lévy过程。纽曼（Newman，1980）的渐近框架仍被用作主要工具。当$ g $是高斯法律时（作为已知结果的确认），而$ g $是托有法律时，则会给出详细的结果。在后来的情况下，独立和相同分布数据的经典结果将扩展到固定和非平稳的相关数据。
The investigation asymptotic limits on associated data mainly focused on limit theorems of summands of associated data and on the related invariance principles. In a series of papers, we are going to set the general frame of the theory by considering an arbitrary infinitely decomposable (divisible) limit law for summands and study the associated functional laws converging to Lévy processes. The asymptotic frame of Newman (1980) is still used as a main tool. Detailed results are given when $G$ is a Gaussian law (as confirmation of known results) and when $G$ is a Poisson law. In the later case, classical results for independent and identically distributed data are extended to stationary and non-stationary associated data.
