This article discusses MLMC estimators with and without weights, applied to nested expectations of the form Ef(EF(Y,Z)|Y ). More precisely, we are interested on the assumptions needed to comply with the MLMC framework, depending on whether the payoff function f is smooth or not. A new result to our knowledge is given when f is not smooth in the development of the weak error at an order higher than 1, which is needed for a successful use of MLMC estimators with weights.

中文翻译：

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嵌套多层蒙特卡洛的微弱误差

本文讨论了带权重和不带权重的MLMC估计器，这些估计器适用于E f（E F（Y，Z）| Y）形式的嵌套期望。更准确地说，我们对符合MLMC框架所需的假设感兴趣，这取决于收益函数f是否平滑。当f在弱误差的发展中不平稳且阶次高于1时，将给出我们所知的新结果，这是成功使用带权重的MLMC估计量所必需的。