An application of the multiplicative Sewing Lemma to the high order weak approximation of stochastic differential equations
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....
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Published in | Stochastic processes and their applications Vol. 165; pp. 183 - 217 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
01.11.2023
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 0304-4149 1879-209X |
DOI: | 10.1016/j.spa.2023.08.006 |