Electronic Communications in Probability

On the completion of Skorokhod space

Mikhail Lifshits and Vladislav Vysotsky

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Abstract

We consider the classical Skorokhod space ${\mathbb {D}}[0,1]$ and the space of continuous functions ${\mathbb {C}}[0,1]$ equipped with the standard Skorokhod distance $\rho $.

It is well known that neither $({\mathbb {D}}[0,1],\rho )$ nor $({\mathbb {C}}[0,1],\rho )$ 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".

Article information

Source
Electron. Commun. Probab., Volume 25 (2020), paper no. 66, 10 pp.

Dates
Received: 26 March 2020
Accepted: 27 August 2020
First available in Project Euclid: 17 September 2020

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1600308260

Digital Object Identifier
doi:10.1214/20-ECP346

Zentralblatt MATH identifier
07252786

Subjects
Primary: 54D35: Extensions of spaces (compactifications, supercompactifications, completions, etc.)
Secondary: 46N30: Applications in probability theory and statistics

Keywords
Skorokhod space Skorokhod distance completion

Rights
Creative Commons Attribution 4.0 International License.

Citation

Lifshits, Mikhail; Vysotsky, Vladislav. On the completion of Skorokhod space. Electron. Commun. Probab. 25 (2020), paper no. 66, 10 pp. doi:10.1214/20-ECP346. https://projecteuclid.org/euclid.ecp/1600308260


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The Institute of Mathematical Statistics and the Bernoulli Society

Electronic Communications in Probability

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