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arXiv · 1812.04583

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

Konstantinos Dareiotis·Máté Gerencsér
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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.

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Konstantinos Dareiotis, Máté Gerencsér. 2018-12-11. On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift. https://doi.org/10.1214/20-ejp479

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