Stieltjes Integrals in Mathematical Statistics

Riemann-Stieltjes integrals

This short note gives an introduction to the Riemann-Stieltjes integral on R and Rn. Some natural and important applications in probability theory are discussed. The reason for discussing the Riemann-Stieltjes integral instead of the more general Lebesgue and LebesgueStieltjes integrals are that most applications in elementary probability theory are satisfactorily covered by the Riemann-Stieltj...

Majorisation inequalities for Stieltjes integrals

Inequalities of the majorisation type for convex functions and Stieltjes integrals are given. Applications for some particular convex functions of interest are also pointed out.

Oregon State College Sequences of Stieltjes Integrals

there is no projection on (m) to (C), it may be shown that at least either there is no projection on (w) to F, or else there is no projection on (m) to the complementary subspace of F in (C). (An illustration of the case where there is no projection on (m) to the complementary subspace in (C) is provided by the case of a finite dimensional YC(Q.) In a paper in preparation on the extension of li...

Cauchy-stieltjes and Riemann-stielt Jes Integrals

Two Point Gauss–legendre Quadrature Rule for Riemann–stieltjes Integrals

In order to approximate the Riemann–Stieltjes integral ∫ b a f (t) dg (t) by 2–point Gaussian quadrature rule, we introduce the quadrature rule ∫ 1 −1 f (t) dg (t) ≈ Af ( − √ 3 3 ) + Bf (√ 3 3 ) , for suitable choice of A and B. Error estimates for this approximation under various assumptions for the functions involved are provided as well.