Year-end Sale % OFF 
Abstract
We show that every mathbb {R}^{d}-valued Sobolev path with regularity α and integrability p can be lifted to a weakly geometric rough path in the sense of T. Lyons with exactly the same regularity and integrability, provided α > 1/p > 0. Moreover, we prove the existence of unique rough path lifts which are optimal w.r.t. strictly convex functionals among all possible rough path lifts given a Sobolev path. This paves a way towards classifying rough path lifts as solutions of optimization problems. As examples, we consider the rough path lift with minimal Sobolev norm and characterize the Stratonovich rough path lift of a Brownian motion as optimal lift w.r.t. a suitable convex functional. Generalizations of the results to Besov spaces are briefly discussed.
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
