Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients

@article{Hutzenthaler2011ConvergenceOT,
  title={Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients},
  author={Martin Hutzenthaler and Arnulf Jentzen},
  journal={Foundations of Computational Mathematics},
  year={2011},
  volume={11},
  pages={657-706}
}
Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. However, the important case of superlinearly growing coefficients has remained an open question. The main difficulty is that numerically weak convergence fails to hold in many cases of superlinearly growing coefficients. In this paper we overcome this difficulty… 

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