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

By Konstantinos Dareiotis, M'at'e Gerencs'er. 2018

53 citations recorded by the source corpus.

The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of $\alpha$-Holder drift in 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 a class of everywhere discontinuous coefficients.

Subfields: Applied Mathematics, Computational Mechanics, Finance

View Paper: https://www.semanticscholar.org/paper/33d8bfc020e21ead04b671566942aa90c13997ff

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In Applied Mathematics

In Computational Mechanics

In Finance

Citations in the corpus

Quantifying a convergence theorem of Gyöngy and Krylov (2021, background): “However, it turned out that this rate is suboptimal: in [9] it is shown that in the additive noise case the rate 1/2 is achieved even for Dini-continuous b, and in dimension d = 1, for merely bounded b.”
Existence of strong solutions for It\^o's stochastic equations via approximations. Revisited (2021, result): “For recent results on the rate of convergence we refer to [2], [14], [17], and the references therein.”