The existence of Riemann-Stieltjes integrals with applications to fractional Brownian motion

TL;DR

This paper establishes new sufficient conditions for the existence of Riemann-Stieltjes integrals, extending classical results and improving recent findings related to fractional Brownian motion with Hurst index greater than 1/2.

Contribution

It provides generalized criteria for Riemann-Stieltjes integral existence, enhancing understanding of integrals involving fractional Brownian motion.

Findings

Derived general sufficient conditions for integral existence

Extended classical Young's conditions

Improved results for fractional Brownian motion with H>1/2

Abstract

We derive general sufficient conditions for the existence of Riemann-Stieltjes integrals $\int_a^b Yd X$. Our results extend the classical conditions of L.C.Young and improve some recent results that deal with integrals involving a fractional Brownian motion with the Hurst index $H>1/2$.