For a strictly stationary sequence of random variables we derive functional convergence of the joint partial sum and partial maxima process under joint regular variation with index $\alpha \in (0,2)$ and weak dependence conditions. The limiting process consists of an α-stable Lévy process and an extremal process. We also describe the dependence between these two components of the limit. The convergence takes place in the space of ${\mathbb{R}}^2$-valued càdlàg functions on $[0,1]$, with the Skorohod weak $M_1$ topology. We further show that this topology in general can not be replaced by the stronger (standard) $M_1$ topology.

对于随机变量的严格平稳序列，我们推导了联合正则变化下具有索引的联合部分和和最大局部过程的函数收敛性 $\alpha \in （0，2）$和弱的依赖条件。极限过程包括一个α稳定的Lévy过程和一个极值过程。我们还描述了限制的这两个组成部分之间的依赖性。收敛发生在${\mathbb{[R}}^2$值的càdlàg函数 $[0，\mathrm{1个}]$，而Skorohod虚弱 ${\mathrm{中号}}_{\mathrm{1个}}$拓扑。我们进一步证明，这种拓扑通常不能被更强的拓扑（标准）取代${\mathrm{中号}}_{\mathrm{1个}}$ 拓扑。