A new theorem on the existence of the Riemann-Stieltjes integral and an improved version of the Loéve-Young inequality

Abstract

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 Loéve-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.

More comprehensive paper, with similar results is "Integration of rough paths - the truncated variation approach, arXiv:1409.3757"

References in corpus (2)

• The Play Operator, the Truncated Variation and the Generalisation of the Jordan Decomposition
• On the Generalisation of the Hahn-Jordan Decomposition for Real Càdlàg Functions

Cited by in corpus (1)

• Riemann-Stieltjes integrals driven by irregular signals in Banach spaces and rate-independent characteristics of their irregularity