A Note on the Notion of Geometric Rough Paths
| dc.creator | Friz, Peter | |
| dc.creator | Victoir, Nicolas | |
| dc.date | 2004-03-06 | |
| dc.date.accessioned | 2026-07-07T05:06:09Z | |
| dc.date.available | 2026-07-07T05:06:09Z | |
| dc.description | We use simple sub-Riemannian techniques to prove that an arbitrary geometric p-rough path in the sense of Lyons (98) 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 definitions of a geometric p-rough path, Lyons (98), Lyons/Qian (02). Our proofs are based on fine estimates in terms of control functions and are sufficiently general to include the case of Hoelder- and modulus-type regularity, Friz/Victoir (03). This allows us to extend a few classical results on Hoelder-spaces (Ciesielski, Musielak/Semadeni) and p-variation spaces (Wiener,Dudley) to the non-commutative setting necessary for the theory of rough paths. | |
| dc.identifier | https://arxiv.org/abs/math/0403115 | |
| dc.identifier | http://arxiv.org/abs/math/0403115 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70375 | |
| dc.subject | Functional Analysis | |
| dc.subject | Probability | |
| dc.subject | 60G17; 53C22; 65D05 | |
| dc.title | A Note on the Notion of Geometric Rough Paths | |
| dc.type | text |