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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]

We provide closed-form expressions for bond prices in interest rate models based on compact Lie groups. Our approach uses a Doob transform technique and PDE solutions by the Mathieu periodic functions. As a by-product, we derive formulas for bond option prices as well as new identities for the Laplace transform of periodic functionals of Brownian motion and Brownian diffusion processes. [ABSTRACT FROM AUTHOR]