231 research outputs found
Approximating the Riemann-Stieltjes Integral via Some Moments of the Integrand
Error bounds in approximating the Riemann-Stieltjes integral in
terms of some moments of the integrand are given. Applications for p-convex
functions and in approximating the Finite Foureir Transform are pointed out
as well
On the approximation of L\'evy driven Volterra processes and their integrals
Volterra processes appear in several applications ranging from turbulence to
energy finance where they are used in the modelling of e.g. temperatures and
wind and the related financial derivatives. Volterra processes are in general
non-semimartingales and a theory of integration with respect to such processes
is in fact not standard. In this work we suggest to construct an approximating
sequence of L\'evy driven Volterra processes, by perturbation of the kernel
function. In this way, one can obtain an approximating sequence of
semimartingales.
Then we consider fractional integration with respect to Volterra processes as
integrators and we study the corresponding approximations of the fractional
integrals. We illustrate the approach presenting the specific study of the
Gamma-Volterra processes. Examples and illustrations via simulation are given.Comment: 39 pages, 3 figure
Bounds for the Riemann–Stieltjes integral via s-convex integrand or integrator
Several bounds in approximating the Riemann–Stieltjes integral in terms of s-convex integrands or integrator are given
Mercer–Trapezoid Rule for the Riemann–Stieltjes Integral with Applications
In this paper several new error bounds for the Mercer - Trapezoid quadrature rule for the Riemann-Stieltjes integral under various assumptions are proved. Applications for functions of selfadjoint operators on complex Hilbert spaces are provided as well
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