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For stochastic differential equations (SDEs) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient, the explicit schemes fail to converge strongly to the exact solution (see, Hutzenthaler, Jentzen and Kloeden in Proc. R. Soc. A, rspa.2010.0348v1–rspa.2010.0348, 2010). In this article a class of implicit methods, called split-step one-leg theta methods (SSOLTM),...
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