Stochastic Bernstein polynomials: uniform convergence in probability with rates
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Fecha
2020-02-27
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Springer
Resumen
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.
Descripción
This version of the article was accepted for publication after peer review. It is subject to
Springer Nature’s AM terms of use. It is not the Version of Record, available online at
https://doi.org/10.1007/s10444-020-09770-6
Palabras clave
Stochastic Bernstein polynomials, Uniform convergence in probability, Rates of convergence, Confidence band, Bernstein-Durrmeyer polynomials
Citación
Adell, J.A., Cárdenas-Morales, D. Stochastic Bernstein polynomials: uniform convergence in probability with rates. Adv Comput Math 46, 16 (2020).