Adaptive Multilevel Monte Carlo Simulation
Adaptive Multilevel Monte Carlo Simulation
复制标题
自适应多级蒙特卡罗模拟
DOI：
10.1007/978-3-642-21943-6_10
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
R. Tempone
中科院分区：
文献类型：
--
作者：
Håkon Hoel;E. Schwerin;A. Szepessy;R. Tempone
这项工作概括了 Michael B. Giles 引入的多级前向欧拉蒙特卡罗方法。 （Michael Giles. Oper. Res. 56(3):607–617, 2008.）根据伊藤随机微分方程的解来近似期望值。这项工作（Michael Giles. Oper. Res. 56(3):607–617, 2008.）提出并分析了一种基于统一时间离散化和控制变量层次结构的前向欧拉多级蒙特卡罗方法，以减少标准、单级前向欧拉蒙特卡罗方法所需的计算量。这项工作介绍了非均匀时间离散化的自适应层次结构，由自适应算法生成（AnnaDzougoutov 等人。Raul Tempone。用于停止扩散的自适应蒙特卡罗算法。在科学和工程中的多尺度方法中，Lect. Notes Comput. Sci. Eng. 第 44 卷，第 59-88 页。Springer，柏林，2005 年；Kyoung-Sook Moon 等人 Stoch. Anal。 Appl. 23(3):511–558, 2005；Kyoung-Sook Moon 等人，《自适应计算的最新进展》，《Contemp Math》第 383 卷，第 325–343 页。这种形式的自适应算法生成随机的、路径相关的时间步长，并且基于首次开发的后验误差扩展（Anders Szepessy et al. Comm. Pure Appl. Math. 54(10):1169–1214, 2001）。我们针对停止扩散问题的数值结果表明，从使用自适应算法的单级版本到 \( \vartheta\left( \begin{array}{lll}\left({(TOL^{-1})\,log(TOL)}\right)^2\end{array}\right).\)
This work generalizes a multilevel forward Euler Monte Carlo method introduced in Michael B. Giles. (Michael Giles. Oper. Res. 56(3):607–617, 2008.) for the approximation of expected values depending on the solution to an Ito stochastic differential equation. The work (Michael Giles. Oper. Res. 56(3):607– 617, 2008.) proposed and analyzed a forward Euler multilevelMonte Carlo method based on a hierarchy of uniform time discretizations and control variates to reduce the computational effort required by a standard, single level, Forward Euler Monte Carlo method. This work introduces an adaptive hierarchy of non uniform time discretizations, generated by an adaptive algorithmintroduced in (AnnaDzougoutov et al. Raul Tempone. Adaptive Monte Carlo algorithms for stopped diffusion. In Multiscale methods in science and engineering, volume 44 of Lect. Notes Comput. Sci. Eng., pages 59–88. Springer, Berlin, 2005; Kyoung-Sook Moon et al. Stoch. Anal. Appl. 23(3):511–558, 2005; Kyoung-Sook Moon et al. An adaptive algorithm for ordinary, stochastic and partial differential equations. In Recent advances in adaptive computation, volume 383 of Contemp. Math., pages 325–343. Amer. Math. Soc., Providence, RI, 2005.). This form of the adaptive algorithm generates stochastic, path dependent, time steps and is based on a posteriori error expansions first developed in (Anders Szepessy et al. Comm. Pure Appl. Math. 54(10):1169– 1214, 2001). Our numerical results for a stopped diffusion problem, exhibit savings in the computational cost to achieve an accuracy of \( \vartheta{\rm(TOL),\, from\,(TOL^{-3})}\), from using a single level version of the adaptive algorithm to \( \vartheta\left( \begin{array}{lll}\left({(TOL^{-1})\,log(TOL)}\right)^2\end{array}\right).\)
影响因子：
2.7
作者：
Giles, Michael B.
通讯作者：
Giles, Michael B.