On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift

DOI10.1214/20-EJP479zbMATH Open1459.60144arXiv1812.04583MaRDI QIDQ2201496

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Publication date: 29 September 2020

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Abstract: The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of $alpha$-H"older drift in the recent literature the rate $alpha/2$ 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 $alpha>0$. The result extends to Dini continuous coefficients, while in $d=1$ also to all bounded measurable coefficients.

Full work available at URL: https://arxiv.org/abs/1812.04583

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