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2020 On the completion of Skorokhod space
Mikhail Lifshits, Vladislav Vysotsky
Electron. Commun. Probab. 25: 1-10 (2020). DOI: 10.1214/20-ECP346

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".

Citation

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Mikhail Lifshits. Vladislav Vysotsky. "On the completion of Skorokhod space." Electron. Commun. Probab. 25 1 - 10, 2020. https://doi.org/10.1214/20-ECP346

Information

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

zbMATH: 07252786
Digital Object Identifier: 10.1214/20-ECP346

Subjects:
Primary: 54D35
Secondary: 46N30

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