Mathematics – Numerical Analysis
Scientific paper
2011-02-03
Mathematics
Numerical Analysis
Accepted by JDEA
Scientific paper
For stochastic differential equations (SDEs) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient, the classical explicit Euler scheme fails to converge strongly to the exact solution. Recently, an explicit strongly convergent numerical scheme, called the tamed Euler method, is proposed in [Hutzenthaler, Jentzen, & Kloeden (2010); Strong convergence of an explicit numerical method for SDEs with non-globally Lipschitz continuous coefficients, arXiv:1010.3756v1] for such SDEs. Motivated by their work, we here introduce a tamed version of the Milstein scheme for SDEs with commutative noise. The proposed method is also explicit and easily implementable, but achieves higher strong convergence order than the tamed Euler method does. In recovering the strong convergence order one of the new method, new difficulties arise and kind of a bootstrap argument is developed to overcome them. Finally, an illustrative example confirms the computational efficiency of the tamed Milstein method compared to the tamed Euler method.
Gan Siqing
Wang Xiaojie
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