We present a simple unifying treatment of a broad class of applications from statistical mechanics, econometrics, mathematical finance, and insurance mathematics, where (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 elucidate 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：我们提出了一套统一的简化处理方法，涵盖统计力学、计量经济学、数学金融和保险数学中的一大类应用，其中（可能从属的）Lévy噪声作为某种连续时间随机游走（CTRW）的标度极限出现。对于每个应用，自然依赖于Skorokhod空间中在J1或M1拓扑下随机积分的弱收敛结果。与早期完全独立的研究相比，我们能够提供更简洁的阐述，同时允许更大的普适性，并给出重要的新见解。对于每个应用，我们首先阐明J1收敛CTRW的基本结论如何作为相同一般原理的特例出现，然后说明具体设置如何为严格M1收敛的CTRW产生不同的结果。