On Tamed Milstein Schemes of SDEs Driven by L\'evy Noise

Abstract

We extend the taming techniques developed in \cite{konstantinos2014,sabanis2013} to construct explicit Milstein schemes that numerically approximate L\'evy 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.