Notes on area operator, geometric 2-rough paths and Young integral when p^-1+q^-1=1

Details Notes on area operator, geometric 2-rough paths and Young integral when p^-1+q^-1=1 Notes on area operator, geometric 2-rough paths and Young integral when p^-1+q^-1=1

2012-03-31

arxiv.org/abs/1204.0112v1

Mathematics

Classical Analysis and ODEs

Scientific paper

1.When equipped with 2-rough norm and restricted to continuous paths with bounded variation, the area operator is a closable unbounded operator. 2.The area defined through Riemann-Stieltjes integral is the only possible candidate to enhance a path with vanishing 2-variation into a geometric 2-rough path. 3.Young integral is extended to p^-1+q^-1=1 by assigning a finer scale continuity.

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