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For GBM you can show it by theory (see Kloeden) or show it empirically as follows. You can observe that EM has strong order of convergence equal to 0.5, whereas Milstein's is 1.0. Not always the latter is superior. E.g. simple EM beats simple Mistein for Heston. In this case is good to use adapted schemes (Giles) for instance, especially dealing with jumps. ...

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