Constrained Rough Paths

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JournalProceedings of the London Mathematical Society
DatePublished - Dec 2015
Issue number6
Volume111
Number of pages48
Pages (from-to)1471-1518
Original languageEnglish

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.

    Research areas

  • math.PR, math.CA, 60H30 (34F05, 58C07, 58J65)

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