Adaptive timestepping strategies for nonlinear stochastic systems

@article{Kelly2016AdaptiveTS,
  title={Adaptive timestepping strategies for nonlinear stochastic systems},
  author={C{\'o}nall Kelly and Gabriel J. Lord},
  journal={arXiv: Numerical Analysis},
  year={2016}
}
  • C. Kelly, G. Lord
  • Published 13 October 2016
  • Mathematics
  • arXiv: Numerical Analysis
We introduce a class of adaptive timestepping strategies for stochastic differential equations with non-Lipschitz drift coefficients. These strategies work by controlling potential unbounded growth in solutions of a numerical scheme due to the drift. We prove that the Euler-Maruyama scheme with an adaptive timestepping strategy in this class is strongly convergent. Specific strategies falling into this class are presented and demonstrated on a selection of numerical test problems. We observe… 
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