Abstract
We define the space of (Holder continuous) rough paths, as well as the subspace of “geometric” rough paths which preserve the usual rules of calculus. The latter can be interpreted in a natural way as paths with values in a certain nilpotent Lie group. At the end of the chapter, we give a short discussion showing how these definitions should be generalized to treat paths of arbitrarily low regularity.
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© 2014 Springer International Publishing Switzerland
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Friz, P.K., Hairer, M. (2014). The space of rough paths. In: A Course on Rough Paths. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-08332-2_2
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DOI: https://doi.org/10.1007/978-3-319-08332-2_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08331-5
Online ISBN: 978-3-319-08332-2
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