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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Bibliographic Details
Published inStochastic processes and their applications Vol. 165; pp. 183 - 217
Main Authors Hocquet, Antoine, Vogler, Alexander
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.11.2023
Subjects
Cubature on Wiener space
Sewing lemma
Weak approximation
Cubature on Wiener space
60H10
Sewing lemma
60G53
60J35
60F05
60G15
Weak approximation
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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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2023.08.006