On convergence of partial derivatives of multivariate Bernstein polynomials
Probability
2016-10-18 v2
Abstract
It is be shown that the sequence of Bernstein polynomials for a function of several variables converges to this function uniformly along with every partial derivative of any order, provided that the latter derivative is well defined and continuous. This may be interesting in some questions of stochastic calculus, in particular, in a methodical proof of multidimensional Ito's formula based on the product rule.
Keywords
Cite
@article{arxiv.1507.05235,
title = {On convergence of partial derivatives of multivariate Bernstein polynomials},
author = {Alexander Veretennikov and Evguenia Veretennikova},
journal= {arXiv preprint arXiv:1507.05235},
year = {2016}
}
Comments
2nd version 19 pages, 17 refs; accepted for publication at Siberian Advances in Mathematics