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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