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arXiv · 1403.5413

A new theorem on the existence of the Riemann-Stieltjes integral and an improved version of the Lo\'eve-Young inequality

Rafał M. Łochowski
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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 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.

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Rafał M. Łochowski. 2014-03-21. A new theorem on the existence of the Riemann-Stieltjes integral and an improved version of the Lo\'eve-Young inequality. https://doi.org/10.1186/s13660-015-0901-3

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