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A quasi-sure non-degeneracy property for the Brownian rough path

Abstract:

In the present paper, we are going to show that outside a slim set in the sense of Malliavin (or quasi-surely), the signature path (which consists of iterated path integrals in every degree) of Brownian motion is non-self-intersecting. This property relates closely to a non-degeneracy property for the Brownian rough path arising naturally from the uniqueness of signature problem in rough path theory. As an important consequence we conclude that quasi-surely, the Brownian rough path does not h...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s11118-018-9699-1

Authors


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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Exeter College
Role:
Author
More from this funder
Funding agency for:
Qian, Z
Grant:
291244 ESig
Publisher:
Springer Netherlands Publisher's website
Journal:
Potential Analysis Journal website
Volume:
51
Issue:
1
Pages:
1–21
Publication date:
2018-05-07
Acceptance date:
2018-04-14
DOI:
EISSN:
1572-929X
ISSN:
0926-2601
Source identifiers:
835665
Keywords:
Pubs id:
pubs:835665
UUID:
uuid:47774622-dc22-4e24-b1fa-e70c82df68da
Local pid:
pubs:835665
Deposit date:
2018-04-14

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