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

Antoine Hocquet; Alexander Vogler

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arXiv · 2206.10297

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

Antoine Hocquet·Alexander Vogler

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Abstract

We introduce a variant of the multiplicative Sewing Lemma in [Gerasimovi\v{c}s, 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.

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Antoine Hocquet, Alexander Vogler. 2022-06-21. An application of the multiplicative Sewing Lemma to the high order weak approximation of stochastic differential equations. https://arxiv.org/abs/2206.10297

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