Search

Complementary regularity between the integrand and integrator is a well known condition for the integral ∫ 0 T f (r) d g (r) to exist in the Riemann-Stieltjes sense. This condition also applies to the multi-dimensional case, in particular the 2 D integral ∫ [ 0 , T ] 2 f (s , t) d g (s , t) . In the paper, we give a new condition for the existence of the integral under the assumption that the integrator g is a Volterra covariance function. We introduce the notion of strong Hölder bi-continuity, and show that if the integrand possess this property, the assumption on complementary regularity can be relaxed for the Riemann-Stieltjes sums of the integral to converge. [ABSTRACT FROM AUTHOR]