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Skorokhod's M1 topology for distribution-valued processes
2016
Electronic Communications in Probability
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Skorokhod's M1 topology is defined for c\'adl\'ag 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 c\'adl\'ag processes. It is shown how this topological space can be used in analysing the convergence of empirical process approximations
doi:10.1214/16-ecp4754
fatcat:h2j2j4ol2nb7nn6ujaexlxkdsu