Skorokhod’s M1 topology for distribution-valued processes

Sean Ledger

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)
276 Downloads (Pure)

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 languageEnglish
Number of pages12
JournalElectronic Communications in Probability
Volume34
DOIs
Publication statusPublished - 21 Apr 2016

Keywords

  • Skorokhod M1 topology
  • compactness and tightness characterisation
  • tempered distribution
  • countably Hilbertian nuclear space

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