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".
Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty