Adell, José A.Cárdenas-Morales, Daniel2024-09-092024-09-092020-02-27Adell, J.A., Cárdenas-Morales, D. Stochastic Bernstein polynomials: uniform convergence in probability with rates. Adv Comput Math 46, 16 (2020).1572-9044 (Electronic) 1019-7168 (Print)10.1007/s10444-020-09770-6https://hdl.handle.net/10953/3180This 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/s10444-020-09770-6We 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.engStochastic Bernstein polynomialsUniform convergence in probabilityRates of convergenceConfidence bandBernstein-Durrmeyer polynomialsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess