Variance Reduction for Simulated Diffusions
Variance Reduction for Simulated Diffusions
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模拟扩散的方差减少
DOI：
10.1137/s0036139992236220
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
Nigel J. Newton
中科院分区：
文献类型：
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作者：
Nigel J. Newton
本文发展了Ito随机微分方程（sdes）解的泛函蒙特卡罗积分的一些方差缩减技术。sdes的蒙特卡罗方法提供了一种计算某些类型抛物型偏微分方程解的方法，因此在随机控制、粒子物理学和计量经济学等各个领域都有应用；它涉及将所需的积分表示为定义在无限维维纳空间上的随机变量的均值，这些随机变量不能直接模拟-它们必须在某个阶段由定义在高维但有限维空间上的变量近似。这里采取的方法是在无限维空间上构造方差减少的随机变量，然后可以用许多已知的有限差分方法中的任何一种来近似。提出了控制变量法和重要抽样法。在这两种情况下，一个完美的变量(即，一个是无偏的和h…
This article develops some variance reduction techniques for the Monte-Carlo integration of functionals of the solutions of Ito stochastic differential equations (sdes). The Monte-Carlo method for sdes offers a means of calculating solutions to certain types of parabolic partial differential equation and so has applications in various fields including stochastic control, particle physics and econometrics; it involves the representation of the required integrals as means of random variables defined on infinite-dimensional Wiener spaces, which cannot be simulated directly—sthey must at some stage be approximated by variables defined on high, but finite-dimensional spaces. The approach taken here is to construct variance reduced random variables on the infinite-dimensional spaces, which can subsequently be approximated by any of a number of known finite difference methods.The methods of control variates and importance sampling are developed. In both cases, a perfect variate (i.e., one which is unbiased and h...