Reconstructions of piece-wise continuous and discrete functions using moments
Statistics Theory
2023-12-08 v1 Classical Analysis and ODEs
Statistics Theory
Abstract
The problem of recovering a moment-determinate multivariate function via its moment sequence is studied. Under mild conditions on , the point-wise and -rates of convergence for the proposed constructions are established. The cases where is the indicator function of a set, and represents a discrete probability mass function are also investigated. Calculations of the approximants and simulation studies are conducted to graphically illustrate the behavior of the approximations in several simple examples. Analytical and simulated errors of proposed approximations are recorded in Tables 1-3.
Cite
@article{arxiv.2312.04462,
title = {Reconstructions of piece-wise continuous and discrete functions using moments},
author = {Robert Mnatsakanov and Rafik Aramyan and Farhad Jafari},
journal= {arXiv preprint arXiv:2312.04462},
year = {2023}
}