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.

中文翻译：

---

随机伯恩斯坦多项式：概率与速率一致收敛

我们介绍与连续函数f相关联的经典伯恩斯坦多项式的随机变体，该函数是由随机变量的一般三角形阵列构成的。我们讨论了它们表示的近似过程的概率的均匀收敛，同时给出了收敛速率。在其中随机变量三角阵列由统一的秩序统计的具体情况，我们给出了一个肯定的答案的一个猜想吴和周（进阶COMPUT，数学，募集46，8，2020年）有关的指数率概率收敛。