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Flow equations on spaces of rough paths

Abstract:

Given an Itô vector fieldM, there is a unique solutionξt(h) to the differential equationdξt(h)dt=M(ξt(h)),ξ0(h)=hfor any continuous and piece-wisely smooth pathh. We show that for anyt∈R, the maph→ξt(h) is continuous in thep-variation topology for anyp≥1, so that it uniquely extends to a solution flow on the space of all geometric rough paths. Applying this result to the Driver's geometric flow equation on the path space over a closed Riemannian manifolddζtdt=Xh(ζt),ξ0=id,whereXhis the vector...

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Publisher copy:
10.1006/jfan.1996.3088

Authors


More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
Journal of Functional Analysis More from this journal
Volume:
149
Issue:
1
Pages:
135-159
Publication date:
1997-09-01
DOI:
ISSN:
0022-1236
Language:
English
Pubs id:
pubs:147134
UUID:
uuid:e71b256f-d9df-498c-a0f0-20764e53282f
Local pid:
pubs:147134
Source identifiers:
147134
Deposit date:
2012-12-19

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