Gyöngy和Krylov的一个收敛定理的量子化

IF 1.4 2区数学 Q2 STATISTICS & PROBABILITY

Annals of Applied Probability Pub Date : 2021-01-28 DOI:10.1214/22-aap1867

Konstantinos Dareiotis, M'at'e Gerencs'er, Khoa Le

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引用次数: 26

摘要

在不给漂移系数施加任何正则性条件的情况下，我们导出了用乘性噪声逼近多维SDE的Euler Maruyama格式的强收敛速度。在噪声是加性的情况下，我们证明了可以利用Sobolev正则性来获得改进的速率：具有$\alpha\In（0,1）$阶正则性的漂移导致速率$（1+\alpha）/2$。

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Quantifying a convergence theorem of Gyöngy and Krylov

We derive sharp strong convergence rates for the Euler-Maruyama scheme approximating multidimensional SDEs with multiplicative noise without imposing any regularity condition on the drift coefficient. In case the noise is additive, we show that Sobolev regularity can be leveraged to obtain improved rate: drifts with regularity of order $\alpha \in (0,1)$ lead to rate $(1+\alpha)/2$.

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来源期刊

Annals of Applied Probability 数学-统计学与概率论

CiteScore

2.70

自引率

5.60%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The Annals of Applied Probability aims to publish research of the highest quality reflecting the varied facets of contemporary Applied Probability. Primary emphasis is placed on importance and originality.