Constrained Rough Paths
File(s)
Accepted version
Published version
Author(s)
Cass, T
Driver, BK
Litterer, C
Type
Journal Article
Abstract
We introduce a notion of rough paths on embedded submanifolds and demonstrate
that this class of rough paths is natural. On the way we develop a notion of
rough integration and an efficient and intrinsic theory of rough differential
equations (RDEs) on manifolds. The theory of RDEs is then used to construct
parallel translation along manifold valued rough paths. Finally, this framework
is used to show there is a one to one correspondence between rough paths on a
d-dimensional manifold and rough paths on d-dimensional Euclidean space. This
last result is a rough path analogue of Cartan's development map and its
stochastic version which was developed by Eeels and Elworthy and Malliavin.
that this class of rough paths is natural. On the way we develop a notion of
rough integration and an efficient and intrinsic theory of rough differential
equations (RDEs) on manifolds. The theory of RDEs is then used to construct
parallel translation along manifold valued rough paths. Finally, this framework
is used to show there is a one to one correspondence between rough paths on a
d-dimensional manifold and rough paths on d-dimensional Euclidean space. This
last result is a rough path analogue of Cartan's development map and its
stochastic version which was developed by Eeels and Elworthy and Malliavin.
Date Issued
2015-12-04
Date Acceptance
2015-08-19
Citation
Proceedings of the London Mathematical Society, 2015, 111 (6), pp.1471-1518
ISSN
1460-244X
Publisher
London Mathematical Society
Start Page
1471
End Page
1518
Journal / Book Title
Proceedings of the London Mathematical Society
Volume
111
Issue
6
Copyright Statement
© 2015 London Mathematical Society. This is an Open Access article distributed under the terms of
the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits
unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits
unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/M00516X/1
Subjects
math.PR
math.PR
math.CA
60H30 (34F05, 58C07, 58J65)
Publication Status
Published