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2020 On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift
Konstantinos Dareiotis, Máté Gerencsér
Electron. J. Probab. 25: 1-18 (2020). DOI: 10.1214/20-EJP479

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 $-Hölder 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. "On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift." Electron. J. Probab. 25 1 - 18, 2020. https://doi.org/10.1214/20-EJP479

Information

Received: 23 June 2019; Accepted: 8 June 2020; Published: 2020
First available in Project Euclid: 16 July 2020

zbMATH: 07252714
MathSciNet: MR4125787
Digital Object Identifier: 10.1214/20-EJP479

Subjects:
Primary: 60H10, 60H35, 65C30

JOURNAL ARTICLE
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