Sentence examples for bounds in the approximation from inspiring English sources

In order to provide sharp error bounds in the approximation rules outlined above, we need the following well-known lemma concerning sharp estimates for the Riemann-Stieltjes integral for various pairs of integrands and integrators (see, for instance, [48]).

Using this method it is possible to establish some bounds in the Poisson approximation for sums (or random sums) of independent integer-valued random vectors.

We derive lower bounds on the approximation errors in terms of the number of Boolean function evaluations.

Subsequently, we derive worst-case bounds on the approximation of the optimum social welfare achieved in (strong) equilibrium by the mechanism.

Bounds on the approximation error of the SDR techniques have been developed in [36], which was motivated by the work in [34].

In the third section, we use the operator method from [4] to establish the bounds for the approximation of Poisson-binomial distribution by Poisson distribution.

We derive Chen Stein error bounds for the approximation.

Recently, Nourdin and Peccati [10, 11] unveiled the surface of the deep connection between the Malliavin calculus and Stein's method in order to derive explicit bounds in the Gaussian and gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian process.

The main aim of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent integer-valued random variables via the Trotter-Renyi distance.

An upper bound of the approximation error is derived in the sense of the supremum norm.

To illustrate the bounds in (37) and the approximations in Lemma 7, we also list there corresponding values of (h^{-1} ( 2pi )), (h^{-1} ( 2pipmpi/2 )), and (( 2pi n-1) pmpi/L )/L) when (L = 1).