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- W4300649095 abstract "In this paper, we build the foundation for a theory of controlled rough paths on manifolds. A number of natural candidates for the definition of manifold valued controlled rough paths are developed and shown to be equivalent. The theory of controlled rough one-forms along such a controlled path and their resulting integrals are then defined. This general integration theory does require the introduction of an additional geometric structure on the manifold which we refer to as a parallelism. The transformation properties of the theory under change of parallelisms is explored. Using these transformation properties, it is shown that the integration of a smooth one-form along a manifold valued controlled rough path is in fact well defined independent of any additional geometric structures. We present a theory of push-forwards and show how it is compatible with our integration theory. Lastly, we give a number of characterizations for solving a rough differential equation when the solution is interpreted as a controlled rough path on a manifold and then show such solutions exist and are unique." @default.
- W4300649095 created "2022-10-03" @default.
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- W4300649095 date "2015-04-13" @default.
- W4300649095 modified "2023-10-18" @default.
- W4300649095 title "Controlled Rough Paths on Manifolds I" @default.
- W4300649095 doi "https://doi.org/10.48550/arxiv.1504.03308" @default.
- W4300649095 hasPublicationYear "2015" @default.
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