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An application of the multiplicative Sewing Lemma to the high order weak approximation of stochastic differential equations

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  • Hocquet, Antoine
  • Vogler, Alexander

Abstract

We introduce a variant of the multiplicative Sewing Lemma in [Gerasimovičs, Hocquet, Nilssen; J. Funct. Anal. 281 (2021)] which yields arbitrary high order weak approximations to stochastic differential equations, extending the cubature approximation on Wiener space introduced by Lyons and Victoir. Our analysis allows to derive stability estimates and explicit weak convergence rates. As a particular example, a cubature approximation for stochastic differential equations driven by continuous Gaussian martingales is given.

Suggested Citation

  • Hocquet, Antoine & Vogler, Alexander, 2023. "An application of the multiplicative Sewing Lemma to the high order weak approximation of stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 183-217.
    • Handle: RePEc:eee:spapps:v:165:y:2023:i:c:p:183-217
    DOI: 10.1016/j.spa.2023.08.006
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    References listed on IDEAS

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    1. Syoiti Ninomiya & Nicolas Victoir, 2008. "Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 107-121.
    2. Passeggeri, Riccardo, 2020. "On the signature and cubature of the fractional Brownian motion for H>12," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1226-1257.
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