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On pathwise quadratic variation for càdlàg functions

Abstract:

We revisit Föllmer’s concept of quadratic variation of a càdlàg function along a sequence of time partitions and discuss its relation with the Skorokhod topology. We show that in order to obtain a robust notion of pathwise quadratic variation applicable to sample paths of càdlàg processes, one must reformulate the definition of pathwise quadratic variation as a limit in Skorokhod topology of discrete approximations along the partition. One then obtains a simpler definition which implies the L...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1214/18-ECP186

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
St Hughs College
ORCID:
0000-0003-1164-6053
Publisher:
Institute of Mathematical Statistics Publisher's website
Journal:
Electronic Communications in Probability Journal website
Volume:
23
Pages:
Article: 85
Publication date:
2018-11-23
Acceptance date:
2018-10-30
DOI:
ISSN:
1083-589X
Pubs id:
pubs:867306
URN:
uri:a191f291-8ff6-42fc-8e26-bdd0e89dc90a
UUID:
uuid:a191f291-8ff6-42fc-8e26-bdd0e89dc90a
Local pid:
pubs:867306

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