A Note on the Notion of Geometric Rough Paths

Abstract

We use simple sub-Riemannian techniques to prove that an arbitrary geometric p-rough path in the sense of [15] is the limit in sup-norm of a sequence of canonically lifted smooth paths, which are uniformly bounded in p-variation, clarifying the two different defintions of a geometric p-rough [15, 16]. Our proofs are based on fine estimates in terms of… (More)

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