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Stochastic Bernstein polynomials: uniform convergence in probability with rates

Fecha

2020-02-27

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ISSN de la revista

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Editor

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).

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