Journal article

### Pathwise integration with respect to paths of finite quadratic variation

Alternative title:
Intégration trajectorielle par rapport à des trajectoires de variation quadratique finie
Abstract:

We study a pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums for gradient-type integrands. We show that the integral satisfies a pathwise isometry property, analogous to the well-known Ito isometry for stochastic integrals. This property is then used to represent the integral as a continuous map on an appropriately defined vector space of integrands. Finally, we obtain a pathwise ‘signal plus noise’ decomposition for r...

Publication status:
Published
Peer review status:
Peer reviewed

### Access Document

Files:
• (Version of record, pdf, 447.8KB)
Publisher copy:
10.1016/j.matpur.2016.10.004

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Hugh's College
Role:
Author
ORCID:
0000-0003-1164-6053
Publisher:
Elsevier Publisher's website
Journal:
Journal de Mathématiques Pures et Appliquées Journal website
Volume:
107
Issue:
6
Pages:
737-757
Publication date:
2016-10-29
Acceptance date:
2016-08-10
DOI:
EISSN:
0021-7824
ISSN:
1776-3371
Source identifiers:
866699
Keywords:
Pubs id:
pubs:866699
UUID:
uuid:bd947570-ddc5-4d67-b96e-1df808a4af5a
Local pid:
pubs:866699
Deposit date:
2018-08-30