论文标题
乘法缝纫引理的应用到随机微分方程的高阶弱近似
An application of the multiplicative Sewing Lemma to the high order weak approximation of stochastic differential equations
论文作者
论文摘要
我们在[Gerasimovičs，Hocquet，Nilssen中引入了多种缝纫引理的变体； J.功能。肛门。 281（2021）]将随机微分方程的任意高阶弱近似值产生，从而扩展了Lyons和Victoir引入的Wiener空间上的Cubature近似。我们的分析允许得出稳定性估计和明确的弱收敛速率。作为一个特殊的例子，给出了由连续高斯球门驱动的随机微分方程的立方体近似。
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.
