论文标题
随机整合方法的一致性
Consistency of randomized integration methods
论文作者
论文摘要
我们证明，一类随机集成方法，包括基于$（t，d）$ - 序列，拉丁超立方体采样，弗洛洛夫点以及Cranley-Patterson旋转的平均值，始终估计对集成功能的期望。这里的一致性是指估计量概率的平均值和/或收敛性的收敛性。此外，我们建议中位修改方法，并在$ l^p $中显示$ p> 1 $一致性，以几乎确定的融合
We prove that a class of randomized integration methods, including averages based on $(t,d)$-sequences, Latin hypercube sampling, Frolov points as well as Cranley-Patterson rotations, consistently estimates expectations of integrable functions. Consistency here refers to convergence in mean and/or convergence in probability of the estimator to the integral of interest. Moreover, we suggest median modified methods and show for integrands in $L^p$ with $p>1$ consistency in terms of almost sure convergence
