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：本文构建了一个可比较多层蒙特卡洛与连续层蒙特卡洛方法的框架。在连续层蒙特卡洛方法中，细化程度由指数分布的随机变量决定，这一特性显著影响计算复杂度。我们提出了一种算法变体，其中指数分布随机变量通过拟蒙特卡洛序列生成，从而实现显著的方差缩减。在所示算例中，准连续层蒙特卡洛算法以明显优势优于多层蒙特卡洛与连续层蒙特卡洛方法。