Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients

@article{Hutzenthaler2010StrongAW,
  title={Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients},
  author={Martin Hutzenthaler and Arnulf Jentzen and Peter E. Kloeden},
  journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  year={2010},
  volume={467},
  pages={1563 - 1576}
}
The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation (SDE) with globally Lipschitz continuous drift and diffusion coefficients. Recent results extend this convergence to coefficients that grow, at most, linearly. For superlinearly growing coefficients, finite-time convergence in the strong mean-square sense remains. In this article, we answer this question to the negative and prove, for a large class of SDEs with non-globally Lipschitz… 

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