Integration of rough paths - the truncated variation approach
Functional Analysis
2014-09-16 v2
Abstract
Using truncated variation techniques we obtain an improved version of the Loeve-Young inequality for the Riemann-Stieltjes integrals driven by rough paths. This allowed us to strenghten some result on the existence of solutions of integral equations driven by moderately irregular signals. We introduce also a new Banach space, containing as a proper subspace the paths with finite -variation, and develop, in a systematic way, several parallel results for the paths from this space, obtained so far for the paths with finite -variation. We start the paper with a general theorem on the existence of the Riemann-Stieltjes integral.
Cite
@article{arxiv.1409.3757,
title = {Integration of rough paths - the truncated variation approach},
author = {Rafał M. Łochowski},
journal= {arXiv preprint arXiv:1409.3757},
year = {2014}
}