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On tamed milstein schemes of SDEs driven by Lévy noise

  • * Corresponding author: Sotirios Sabanis

    * Corresponding author: Sotirios Sabanis
This work was done when the first author was a PhD student in the School of Mathematics, University of Edinburgh, United Kingdom.
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  • We extend the taming techniques developed in [3,19] to construct explicit Milstein schemes that numerically approximate Lévy driven stochastic differential equations with super-linearly growing drift coefficients. The classical rate of convergence is recovered when the first derivative of the drift coefficient satisfies a polynomial Lipschitz condition.

    Mathematics Subject Classification: Primary:60H35;secondary:65C30.


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  • Figure 1.  $\mathcal{L}^q$-convergence rate of tamed Milstein scheme (60) of SDE (59)

    Figure 2.  $\mathcal{L}^2$-convergence rate of tamed Milstein scheme (62) of SDE (61)

    Table 1.  Tamed Milstein scheme (60) of SDE (59)

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    Table 2.  Tamed Milstein scheme (62) of SDE (61)

    (A) Mark is normal with mean $0$ and variance $0.125$.
    (B) Mark is uniform on $[-1/4,1/4]$.
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