Open Access
June 2023 Quantifying a convergence theorem of Gyöngy and Krylov
Konstantinos Dareiotis, Máté Gerencsér, Khoa Lê
Author Affiliations +
Ann. Appl. Probab. 33(3): 2291-2323 (June 2023). DOI: 10.1214/22-AAP1867


We derive sharp strong convergence rates for the Euler–Maruyama scheme approximating multidimensional SDEs with multiplicative noise without imposing any regularity condition on the drift coefficient. In case the noise is additive, we show that Sobolev regularity can be leveraged to obtain improved rate: drifts with regularity of order α(0,1) lead to rate (1+α)/2.

Funding Statement

The third author was supported by Alexander von Humboldt Research Fellowship and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 683164).


The authors would like to thank the referees for their especially careful reading and many suggestions.


Download Citation

Konstantinos Dareiotis. Máté Gerencsér. Khoa Lê. "Quantifying a convergence theorem of Gyöngy and Krylov." Ann. Appl. Probab. 33 (3) 2291 - 2323, June 2023.


Received: 1 February 2021; Revised: 1 March 2022; Published: June 2023
First available in Project Euclid: 2 May 2023

MathSciNet: MR4583671
zbMATH: 1511.60102
Digital Object Identifier: 10.1214/22-AAP1867

Primary: 60H10 , 60H35 , 60H50

Keywords: Euler–Maruyama scheme , rate of convergence , regularisation by noise , Stochastic differential equations , strong approximation

Rights: Copyright © 2023 Institute of Mathematical Statistics

Vol.33 • No. 3 • June 2023
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