Ledger, Sean Skorokhod’s M1 topology for distribution-valued processes. (English) Zbl 1338.60105 Electron. Commun. Probab. 21, Paper No. 34, 11 p. (2016). Summary: Skorokhod’s M1 topology is defined for càdlàg paths taking values in the space of tempered distributions (more generally, in the dual of a countably Hilbertian nuclear space). Compactness and tightness characterisations are derived which allow us to study a collection of stochastic processes through their projections on the familiar space of real-valued càdlàg processes. It is shown how this topological space can be used in analysing the convergence of empirical process approximations to distribution-valued evolution equations with Dirichlet boundary conditions. Cited in 4 Documents MSC: 60G07 General theory of stochastic processes 60F17 Functional limit theorems; invariance principles Keywords:Skorokhod M1 topology; compactness characterisation; tightness characterisation; tempered distribution; countably Hilbertian nuclear space PDFBibTeX XMLCite \textit{S. Ledger}, Electron. Commun. Probab. 21, Paper No. 34, 11 p. (2016; Zbl 1338.60105) Full Text: DOI arXiv Euclid