具有不规则漂移的Euler-Maruyama格式的噪声正则化
On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift
摘要：
研究了具有不规则漂移系数的非退化偏微分方程的Euler-Maruyama格式的强收敛速率。在$α$ -赫尔德漂移的情况下，在最近的文献中，速率$α/2$在许多相关情况下得到了证明。通过更有效地利用噪声的正则化效应，我们证明了对于所有$α>0$，速率实际上任意接近于$1/2$。结果推广到Dini连续系数，而在$d=1$中也推广到所有有界可测系数.
英文摘要：
The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of $α$-Hölder drift in the recent literature the rate $α/2$ was proved in many related situations. By exploiting the regularising effect of the noise more efficiently, we show that the rate is in fact arbitrarily close to $1/2$ for all $α>0$. The result extends to Dini continuous coefficients, while in $d=1$ also to all bounded measurable coefficients.
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