High order recombination and an application to cubature on Wiener space
High order recombination and an application to cubature on Wiener space
复制标题
高阶复合及其在维纳空间立方体中的应用
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
T. Lyons
中科院分区：
文献类型：
--
作者：
C. Litterer;T. Lyons
粒子方法被广泛使用，因为它们可以提供对演化度量的准确描述。最近，很明显，通过跳出蒙特卡罗范式，这些方法可以具有更高的阶数，并具有有效且透明的误差范围。粒子方法（特别是在高阶情况下）的一个弱点是，如果迭代过程并保持精度，则粒子数量倾向于爆炸。在本文中，我们确定了一种新方法，该方法允许在此类方法中进行动态重组，并通过简化迭代中使用的中间度量的支持来保留高阶精度。我们描述了一种算法，可用于简化离散测度的支持，并应用于由 Lyons 和 Victoir 开发的维纳空间方法的立方体 [Proc. R.苏克。伦敦。序列。数学。物理。工程师。科学。 460（2004）169-198]。
Particle methods are widely used because they can provide accurate descriptions of evolving measures. Recently it has become clear that by stepping outside the Monte Carlo paradigm these methods can be of higher order with effective and transparent error bounds. A weakness of particle methods (particularly in the higher order case) is the tendency for the number of particles to explode if the process is iterated and accuracy preserved. In this paper we identify a new approach that allows dynamic recombination in such methods and retains the high order accuracy by simplifying the support of the intermediate measures used in the iteration. We describe an algorithm that can be used to simplify the support of a discrete measure and give an application to the cubature on Wiener space method developed by Lyons and Victoir [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460 (2004) 169-198].