We present a simple unifying treatment of a large class of applications from statistical mechanics, econometrics, mathematical finance, and insurance mathematics, where stable (possibly subordinated) L\'evy noise arises as a scaling limit of some form of continuous-time random walk (CTRW). For each application, it is natural to rely on weak convergence results for stochastic integrals on Skorokhod space in Skorokhod's J1 or M1 topologies. As compared to earlier and entirely separate works, we are able to give a more streamlined account while also allowing for greater generality and providing important new insights. For each application, we first make clear how the fundamental conclusions for J1 convergent CTRWs emerge as special cases of the same general principles, and we then illustrate how the specific settings give rise to different results for strictly M1 convergent CTRWs.

翻译：我们提出一种统一的简化处理方法，涵盖统计力学、计量经济学、数理金融和保险数学中大量应用场景——其中稳定（可能次协调的）李维噪声作为某种连续时间随机游走的尺度极限出现。针对每个应用场景，自然需要依托Skorokhod空间上J1或M1拓扑下随机积分的弱收敛结果。相较于此前完全独立的研究，我们能够提供更简明的论述，同时实现更高普适性并给出重要新见解。对于每个应用场景，我们首先阐明J1收敛的连续时间随机游走的基本结论如何作为相同一般原理的特例出现，进而展示特定设置如何对严格M1收敛的连续时间随机游走产生不同结果。