量化(信号处理)
方差减少
数学
重要性抽样
高斯分布
应用数学
分层抽样
估计员
采样(信号处理)
二次方程
数学优化
蒙特卡罗方法
统计物理学
算法
计算机科学
统计
物理
滤波器(信号处理)
量子力学
计算机视觉
几何学
作者
Sylvain Corlay,Gilles Pagès
出处
期刊:Monte Carlo Methods and Applications
[De Gruyter]
日期:2015-02-06
卷期号:21 (1): 1-32
被引量:10
标识
DOI:10.1515/mcma-2014-0010
摘要
Abstract In this article, we propose several quantization-based stratified sampling methods to reduce the variance of a Monte Carlo simulation. Theoretical aspects of stratification lead to a strong link between optimal quadratic quantization and the variance reduction that can be achieved with stratified sampling. We first put the emphasis on the consistency of quantization for partitioning the state space in stratified sampling methods in both finite and infinite-dimensional cases. We show that the proposed quantization-based strata design has uniform efficiency among the class of Lipschitz continuous functionals. Then a stratified sampling algorithm based on product functional quantization is proposed for path-dependent functionals of multi-factor diffusions. The method is also available for other Gaussian processes such as Brownian bridge or Ornstein–Uhlenbeck processes. We derive in detail the case of Ornstein–Uhlenbeck processes. We also study the balance between the algorithmic complexity of the simulation and the variance reduction factor.
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