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August 2012 High order recombination and an application to cubature on Wiener space
C. Litterer, T. Lyons
Ann. Appl. Probab. 22(4): 1301-1327 (August 2012). DOI: 10.1214/11-AAP786


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].


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C. Litterer. T. Lyons. "High order recombination and an application to cubature on Wiener space." Ann. Appl. Probab. 22 (4) 1301 - 1327, August 2012.


Published: August 2012
First available in Project Euclid: 10 August 2012

zbMATH: 1261.65011
MathSciNet: MR2985162
Digital Object Identifier: 10.1214/11-AAP786

Primary: 65C30

Rights: Copyright © 2012 Institute of Mathematical Statistics


Vol.22 • No. 4 • August 2012
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