APPROXIMATING MIXED HOLDER FUNCTIONS USING RANDOM SAMPLES
成果类型：
Article
署名作者：
Marshall, Nicholas F.
署名单位：
Yale University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/19-AAP1471
发表日期：
2019
页码：
2988-3005
关键词：
摘要：
Suppose f : [0, 1](2) -> R is a (c, alpha)-mixed Holder function that we sample at l points X-1,..., X-l chosen uniformly at random from the unit square. Let the location of these points and the function values f(X-1),..., f(X-l) be given. If l >= c(1)n log(2)n, then we can compute an approximation (f) over tilde such that parallel to integral -(integral) over tilde parallel to L-2 = O(n(-alpha) log(3/2)n), with probability at least 1- n(2-c1), where the implicit constant only depends on the constants c > 0 and c(1) > 0.
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