Polynomial convergence order of stochastic Bernstein approximation
Polynomial convergence order of stochastic Bernstein approximation
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DOI：
10.1007/s10444-020-09742-w
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发表时间：
2020-02
影响因子：
1.7
通讯作者：
Zongmin Wu;Xuan Zhou
中科院分区：
文献类型：
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作者：
Zongmin Wu;Xuan Zhou
最近，Wu等人（Adv. Comput. Math.38：187-205，2013）研究了基于随机采样的伯恩斯坦多项式逼近方案，并获得了基础随机变量在连续模方面的六阶矩估计。在本文中，我们采用了一种新的技术，并建立所有偶数阶矩的估计。我们的工作给出了一个强有力的迹象表明，随机伯恩斯坦逼近的概率收敛速度是指数的模的连续性，我们离开作为一个猜想在文件的最后。
Recently, authors of Wu et al. (Adv. Comput. Math.38:187-205, 2013) studied a Bernstein polynomial approximation scheme based on stochastic sampling and obtained a sixth-order moment estimate for the underlying random variable in terms of the modulus of continuity. In the current paper, we employ a new technique and establish estimates for all the even-order moments. Our work gives a strong indication that the probabilistic convergence rate of the stochastic Bernstein approximation is exponential with respect to the modulus of continuity, which we leave as a conjecture at the end of the paper.