We study the joint limit behavior of sums, maxima and $\ell^p$-type moduli for samples taken from an $\mathbb{R}^d$-valued regularly varying stationary sequence with infinite variance. As a consequence, we can determine the distributional limits for ratios of sums and maxima, studentized sums, and other self-normalized quantities in terms of hybrid characteristic functions and Laplace transforms. These transforms enable one to calculate moments of the limits and to characterize the differences between the iid and stationary cases in terms of indices which describe effects of extremal clustering on functionals acting on the dependent sequence.

翻译：我们研究了取自无穷方差、取值为$\mathbb{R}^d$的正则变化平稳序列的样本的和、最大值及$\ell^p$型模量的联合极限行为。作为推论，我们可以用混合特征函数和拉普拉斯变换确定和与最大值之比、学生化总和及其他自标准化量的分布极限。这些变换使人们能够计算极限的矩，并通过描述极值聚类对作用于相依序列的函数的影响的指标，刻画独立同分布情形与平稳情形之间的差异。