# Error estimates of the backward Euler–Maruyama method for multi-valued stochastic differential equations

@article{Eisenmann2019ErrorEO, title={Error estimates of the backward Euler–Maruyama method for multi-valued stochastic differential equations}, author={Monika Eisenmann and Mih{\'a}ly Kov{\'a}cs and Raphael Kruse and Stig Larsson}, journal={BIT Numerical Mathematics}, year={2019}, volume={62}, pages={803 - 848} }

In this paper we derive error estimates of the backward Euler–Maruyama method applied to multi-valued stochastic differential equations. An important example of such an equation is a stochastic gradient flow whose associated potential is not continuously differentiable but assumed to be convex. We show that the backward Euler–Maruyama method is well-defined and convergent of order at least 1/4 with respect to the root-mean-square norm. Our error analysis relies on techniques for deterministic…

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