%0 Journal Article
%T A new theorem on the existence of the Riemann-Stieltjes integral and an improved version of the Lo¨¦ve-Young inequality
%A Rafa£¿ M. £¿ochowski
%J Mathematics
%D 2014
%I arXiv
%R 10.1186/s13660-015-0901-3
%X Using the notion of the truncated variation we obtain a new theorem on the existence and estimation of the Riemann-Stieltjes integral. As a special case of this theorem we obtain an improved version of the Lo\'{e}ve-Young inequality for the Riemann-Stieltjes integrals driven by irregular signals. Using this result we strenghten some results of Terry Lyons on the existence of solutions of integral equations driven by moderately irregular signals.
%U http://arxiv.org/abs/1403.5413v4