Quantifying a convergence theorem of Gyöngy and Krylov

By Konstantinos Dareiotis, M'at'e Gerencs'er, Khoa Le. The Annals of Applied Probability, 2021

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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 $\alpha \in (0,1)$ lead to rate $(1+\alpha)/2$.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/b23d7321d2197cbaac82b2a9ce727d6463286f0d