Abstract
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.
Original language | English |
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Number of pages | 12 |
Journal | Electronic Communications in Probability |
Volume | 34 |
DOIs | |
Publication status | Published - 21 Apr 2016 |
Keywords
- Skorokhod M1 topology
- compactness and tightness characterisation
- tempered distribution
- countably Hilbertian nuclear space