For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a stable, non-Gaussian limit. The obtained limit theorem admits a natural extension to the functional convergence in Skorokhod's $M_1$ topology.

中文翻译：

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相关规律变化序列的稳定极限

对于有规律变化和相关联的平稳序列，我们给出了保证该序列的部分和，在与规律变化指数相关的归一化下，分布收敛到稳定的非高斯极限的条件。所获得的极限定理允许对 Skorokhod 的 $M_1$ 拓扑中的函数收敛进行自然扩展。