Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients

@article{Hutzenthaler2012StrongCO,
  title={Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients},
  author={Martin Hutzenthaler and Arnulf Jentzen and Peter E. Kloeden},
  journal={Annals of Applied Probability},
  year={2012},
  volume={22},
  pages={1611-1641}
}
On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient. On the other hand, the implicit Euler scheme is known to converge strongly to the exact solution of such an SDE. Implementations of the implicit Euler scheme, however, require additional computational effort. In this article we therefore propose an explicit and easily… 

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Abstract A method is proposed for the numerical solution of Itô stochastic differential equations by means of a second-order Runge–Kutta iterative scheme rather than the less efficient Euler
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