2015/09/30 by Sean Ledger · 1 citation
Mathematics · #math.PR
paper · pdf · doi:10.1214/16-ecp4754
published as Electronic Communications in Probability, Vol. 21, No. 34, pp 1-11, 2016 · 13 pages, 2 figures
arxiv created 2016/11/08 · arxiv updated 2016/11/09
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.