Multilevel Monte Carlo methods
Multilevel Monte Carlo methods
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DOI：
10.1017/s096249291500001x
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发表时间：
2015-01-01
期刊：
影响因子：
14.2
通讯作者：
Giles, Michael B.
中科院分区：
文献类型：
--
作者：
Giles, Michael B.
蒙特卡罗方法是一种非常通用和有用的方法，用于估计随机模拟产生的期望值。然而，这些方法的计算成本很高，尤其是当生成单个随机样本的成本很高时，如随机 PDE 的情况。在本文中，我们将回顾多级蒙特卡洛方法背后的思想，以及最近的各种概括和扩展，并讨论一些应用，这些应用说明了该方法的灵活性和通用性，以及在开发收敛速度更快的多级修正方差的更高效实现方法方面所面临的挑战。
Monte Carlo methods are a very general and useful approach for the estimation of expectations arising from stochastic simulation. However, they can be computationally expensive, particularly when the cost of generating individual stochastic samples is very high, as in the case of stochastic PDEs. Multilevel Monte Carlo is a recently developed approach which greatly reduces the computational cost by performing most simulations with low accuracy at a correspondingly low cost, with relatively few simulations being performed at high accuracy and a high cost.In this article, we review the ideas behind the multilevel Monte Carlo method, and various recent generalizations and extensions, and discuss a number of applications which illustrate the flexibility and generality of the approach and the challenges in developing more efficient implementations with a faster rate of convergence of the multilevel correction variance.