Skorokhod's M1 topology for distribution-valued processes
| Autor: | Ledger, Sean |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Electronic Communications in Probability, Vol. 21, No. 34, pp 1-11, 2016 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1214/16-ECP4754 |
| Popis: | 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 to distribution-valued evolution equations with Dirichlet boundary conditions. Comment: 13 pages, 2 figures |
| Databáze: | arXiv |
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