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 $(1+\alpha )/2$.

arXiv comment36 pages, revised version. Section 1.4. added on to some extent degenerate/growing coefficients

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Cited by in corpus (8)

• Taming singular stochastic differential equations: A numerical method
• Path-by-path regularisation through multiplicative noise in rough, Young, and ordinary differential equations
• Optimal rate of convergence for approximations of SPDEs with non-regular drift
• Existence of strong solutions for Itô's stochastic equations via approximations. Revisited
• Bicausal optimal transport for SDEs with irregular coefficients
• Stochastic sewing in Banach space
• 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