(Springer, 2020-02-27) Adell, José A.; Cárdenas-Morales, Daniel
We introduce stochastic variants of the classical Bernstein polynomials associated
with a continuous function f , built up from a general triangular array of random
variables. We discuss the uniform convergence in probability of the approximation
process that they represent, providing at the same time rates of convergence. In the
particular case in which the triangular array of random variables consists of the uniform
order statistics, we give a positive answer to a conjectured raised in Wu and
Zhou (Adv. Comput. Math. 46, 8, 2020) about an exponential rate of convergence in
probability.
