Monte Carlo and Quasi-Monte Carlo Methods 2012
Monte Carlo and Quasi-Monte Carlo Methods 2012
复制标题
蒙特卡罗和准蒙特卡罗方法 2012
DOI：
10.1007/978-3-642-41095-6_4
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Giles M
中科院分区：
文献类型：
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作者：
Giles M
蒙特卡罗方法是一种非常通用且有用的方法，用于估计随机模拟产生的期望。然而，它们的计算成本可能很高，特别是当生成单个随机样本的成本非常高时（如随机偏微分方程的情况）。多级蒙特卡罗是一种最近开发的方法，它通过以相对较低的成本执行大多数低精度模拟，而以高精度和高成本执行相对较少的模拟，从而大大降低了计算成本。在本文中，我们回顾了多级蒙特卡罗方法背后的思想，以及最近的各种概括和扩展，并讨论了一些应用，这些应用说明了该方法的灵活性和通用性，以及开发具有更快的多级校正方差收敛速度的更有效实现的挑战。
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.