# 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={M. Hutzenthaler and A. Jentzen and P. 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… Expand

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#### References

SHOWING 1-10 OF 44 REFERENCES

Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations

- Mathematics, Computer Science
- SIAM J. Numer. Anal.
- 2002

504 Highly Influential- PDF

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

- Mathematics
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2010

255- PDF

Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients

- Mathematics, Computer Science
- Found. Comput. Math.
- 2011

32- PDF

A Note on the Rate of Convergence of the Euler–Maruyama Method for Stochastic Differential Equations

- Mathematics
- 2008

19 Highly Influential

Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients

- Mathematics
- 2013

85- PDF

Pathwise Accuracy and Ergodicity of Metropolized Integrators for SDEs

- Mathematics, Physics
- 2009

63 Highly Influential- PDF