The space of rough paths
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We define the space of (H¨older 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 generalised to treat paths of arbitrarily low regularity.
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