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Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity

Abstract:

We construct a pathwise integration theory, associated with a change of variable formula, for smooth functionals of continuous paths with arbitrary regularity defined in terms of the notion of $p$-th variation along a sequence of time partitions. For paths with finite $p$-th variation along a sequence of time partitions, we derive a change of variable formula for $p$ times continuously differentiable functions and show pointwise convergence of appropriately defined compensated Riemann sums. R...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1090/btran/34

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
St Hugh's College
Role:
Author
ORCID:
0000-0003-1164-6053
Publisher:
American Mathematical Society Publisher's website
Journal:
Transactions of the American Mathematical Society Journal website
Volume:
6
Issue:
6
Pages:
161-186
Publication date:
2019-04-10
Acceptance date:
2018-09-28
DOI:
EISSN:
1088-6850
ISSN:
0002-9947
Source identifiers:
867305
Keywords:
Pubs id:
pubs:867305
UUID:
uuid:e11a9602-21e3-460b-9920-5ca0251cc04f
Local pid:
pubs:867305
Deposit date:
2018-08-30

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