Quantifying a convergence theorem of Gyöngy and Krylov

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

36 pages, revised version. Section 1.4. added on to some extent degenerate/growing coefficients

References in corpus (3)

• Singular paths spaces and applications
• Taming singular stochastic differential equations: A numerical method
• Convergence rate of EM algorithm for SDEs under integrability condition

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• Convergence rate of numerical scheme for SDEs with a distributional drift in Besov space
• Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-norms