This paper provides a framework in which multilevel Monte Carlo and continuous level Monte Carlo can be compared. In continuous level Monte Carlo the level of refinement is determined by an exponentially distributed random variable, which therefore heavily influences the computational complexity. We propose in this paper a variant of the algorithm, where the exponentially distributed random variable is generated by a quasi Monte Carlo sequence, resulting in a significant variance reduction. In the examples presented the quasi continuous level Monte Carlo algorithm outperforms multilevel and continuous level Monte Carlo by a clear margin.

翻译：本文提出了一个框架，用于比较多层蒙特卡洛方法与连续层次蒙特卡洛方法。在连续层次蒙特卡洛方法中，细化层次由指数分布随机变量决定，这显著影响了计算复杂度。本文提出了一种算法变体，其中指数分布随机变量通过准蒙特卡洛序列生成，从而实现了显著的方差缩减。在实例分析中，准连续层次蒙特卡洛方法在性能上明显优于多层蒙特卡洛和连续层次蒙特卡洛方法。