HIGH ORDER RECOMBINATION AND AN APPLICATION TO CUBATURE ON WIENER SPACE
成果类型：
Article
署名作者：
Litterer, C.; Lyons, T.
署名单位：
Imperial College London; University of Oxford; University of Oxford
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/11-AAP786
发表日期：
2012
页码：
1301-1327
关键词：
摘要：
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].