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Cubature on Wiener Space Continued

In: Stochastic Processes And Applications To Mathematical Finance

Author

Listed:
  • Christian Litterer

    (Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB, UK)

  • Terry Lyons

    (Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB, UK)

Abstract

Higher order particle methods can provide an accurate description of an evolving family of measures, but frequently the number of particles used in the description explodes as we iterate. In this paper we present a general method to simplify the support of the intermediate measures used in the iteration without increasing the error in the particle approximation by more than a constant factor. We describe two algorithms 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, Victoir [13].

Suggested Citation

  • Christian Litterer & Terry Lyons, 2007. "Cubature on Wiener Space Continued," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 12, pages 197-217, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812770448_0012
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    Cited by:

    1. Christian Bayer & Peter K. Friz, 2013. "Cubature on Wiener space: pathwise convergence," Papers 1304.4623, arXiv.org.
    2. Qi Feng & Jianfeng Zhang, 2021. "Cubature Method for Stochastic Volterra Integral Equations," Papers 2110.12853, arXiv.org, revised Jul 2023.

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