In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential models by the MLMC method. We follow the approach of (reference), which recasts the estimation of the above quantities to the computation of suitable parametric expectations. In this work, we present novel computable error estimators for the estimation of such quantities, which are then used to optimally tune the MLMC hierarchy in a continuation type adaptive algorithm. We demonstrate the efficiency and robustness of our adaptive continuation-MLMC in an array of numerical test cases.

翻译：本文考虑通过MLMC方法估计复杂随机微分模型输出量的概率分布、分位数或分位数以上的条件期望（即条件风险价值）。我们沿用（参考文献）的方法，将上述量的估计重构为对适当参数化期望值的计算。本文针对此类量的估计提出了新颖的可计算误差估计子，并将其用于以连续型自适应算法最优调整MLMC层级结构。我们通过一系列数值测试案例验证了所提出的自适应连续-MLMC方法的效率与稳健性。