On Tamed Euler Approximations of SDEs Driven by Lévy Noise with Applications to Delay Equations

Abstract: We extend the taming techniques for explicit Euler approximations of stochastic differential equations (SDEs) driven by L\'evy noise with super-linearly growing drift coefficients. Strong convergence results are presented for the case of locally Lipschitz coefficients. Moreover, rate of convergence results are obtained in agreement with classical literature when the local Lipschitz continuity assumptions are replaced by global and, in addition, the drift coefficients satisfy polynomial Lipschitz continuity. Finally, we further extend these techniques to the case of delay equations.