Related papers: On the paper "statistical approximation by positiv…
withdrawed due to a substantial error.
In this paper author was proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted…
This paper proposes to develop a new variant of the two-time-scale stochastic approximation to find the roots of two coupled nonlinear operators, assuming only noisy samples of these operators can be observed. Our key idea is to leverage…
This short note provides a new and simple proof of the convergence rate for Peng's law of large numbers under sublinear expectations, which improves the corresponding results in Song [15] and Fang et al. [3].
We have observed a gap in one of the arguments in the main theorem. We choose to withdraw the paper until we rectify the gap.
In their IZA Discussion Paper 10247, Johansson and Lee claim that the main result (Proposition 3) in Abbring and Van den Berg (2003b) does not hold. We show that their claim is incorrect. At a certain point within their line of reasoning,…
We study in this paper the function approximation error of linear interpolation and extrapolation. Several upper bounds are presented along with the conditions under which they are sharp. All results are under the assumptions that the…
This paper has been withdrawn by the author, due to a crucial error in page 5.
his paper deals with approximating properties of the newly defined $q$-generalization of the Sz\'{a}sz operators in the case $q>1$. Quantitative estimates of the convergence in the polynomial weighted spaces and the Voronovskaja's theorem…
We consider approximation problems for tensor product and additive random fields based on standard information in the average case setting. We also study the probabilistic setting of the mentioned problem for tensor products. The main…
TD($\lambda$) with function approximation has proved empirically successful for some complex reinforcement learning problems. For linear approximation, TD($\lambda$) has been shown to minimise the squared error between the approximate value…
First, we consider generalized wave and scattering operators and derive modifications of commutation relations (between scattering operators and unperturbed operators) when the corresponding deviation factors behave as $\exp\{i t {\mathcal…
We prove that an operator system $\mathcal S$ is nuclear in the category of operator systems if and only if there exist nets of unital completely positive maps $\phi_\lambda : \cl S \to M_{n_\lambda}$ and $\psi_\lambda : M_{n_\lambda} \to…
Paper withdrawn by the author after learning that its main conclusion was given earlier in a slightly different language in Appendix D of A. J. Buras, R. Fleischer, S. Recksiegel, and F.Schwab, hep-ph/0402112.
We study the first-order probabilistic programming language introduced by Staton et al. (2016), but with an additional language construct, $\mathbf{stat}$, that, like the fixpoint operator of Atkinson et al. (2018), converts the description…
We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the…
This note provides a new approach to a result of Foregger and related earlier results by Keilson and Eberlein. Using quite different techniques, we prove a more general result from which the others follow easily. Finally, we argue that the…
This paper has been withdrawn by the author due to a crucial error in the proof of Theorem 1.
This paper has been withdrawn by the author due to a serious mistake on Lemma 2.4.
The goal of this paper is to provide a theory linear regression based entirely on approximations. It will be argued that the standard linear regression model based theory whether frequentist or Bayesian has failed and that this failure is…