Quantifying a convergence theorem of Gyöngy and Krylov

DOI10.1214/22-AAP1867zbMATH Open1511.60102arXiv2101.12185WikidataQ123113696 ScholiaQ123113696MaRDI QIDQ6104027

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Publication date: 5 June 2023

Published in: (Search for Journal in Brave)

Abstract: 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 $alphain(0,1)$ lead to rate $(1+alpha)/2$.

Full work available at URL: https://arxiv.org/abs/2101.12185

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