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：在这项工作中,我们考虑了估算由MLMC方法得出的复杂随机差分模型产出量的概率分布、量化或附条件的预期值高于四分位数的问题,即所谓的有条件值风险。我们遵循了(参考)方法,将上述数量的估计值重新调整为适当的参数预期值的计算。在这项工作中,我们提出了新的可计算误差估计值,然后用一种持续适应性算法优化MLMC等级。我们在一系列数字测试案例中显示了我们的适应性持续-MLMC的效率和稳健性。