# On stochastic differential equations with arbitrary slow convergence rates for strong approximation

@article{Jentzen2015OnSD, title={On stochastic differential equations with arbitrary slow convergence rates for strong approximation}, author={Arnulf Jentzen and Thomas Muller-Gronbach and Larisa Yaroslavtseva}, journal={arXiv: Numerical Analysis}, year={2015} }

In the recent article [Hairer, M., Hutzenthaler, M., Jentzen, A., Loss of regularity for Kolmogorov equations, Ann. Probab. 43 (2015), no. 2, 468--527] it has been shown that there exist stochastic differential equations (SDEs) with infinitely often differentiable and globally bounded coefficients such that the Euler scheme converges to the solution in the strong sense but with no polynomial rate. Hairer et al.'s result naturally leads to the question whether this slow convergence phenomenon…

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## 39 Citations

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ABSTRACT In recent work of Hairer, Hutzenthaler and Jentzen, [11], a stochastic differential equation (SDE) with infinitely differentiable andbounded coefficients was constructed such that the Monte…

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