On the completion of skorokhod space

Mikhail Lifshits, Vladislav Vysotsky

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the classical Skorokhod space D[0, 1] and the space of continuous functions C[0, 1] equipped with the standard Skorokhod distance ρ. It is well known that neither (D[0, 1], ρ) nor (C[0, 1], ρ) is complete. We provide an explicit description of the corresponding completions. The elements of these completions can be regarded as usual functions on [0, 1] except for a countable number of instants where their values vary “instantly".

Original languageEnglish
Article number66
Pages (from-to)1-10
Number of pages10
JournalElectronic Communications in Probability
Volume25
DOIs
StatePublished - 2020

Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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