231 research outputs found

    Approximating the Riemann-Stieltjes Integral via Some Moments of the Integrand

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    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

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    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

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    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

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    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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