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

TL;DR

This paper develops explicit Milstein schemes with taming techniques for numerically solving Le9vy-driven SDEs with super-linear drift, achieving classical convergence rates under certain conditions.

Contribution

It extends taming methods to Milstein schemes for Le9vy SDEs, enabling explicit approximation with optimal convergence rates.

Findings

Achieves classical convergence rate under polynomial Lipschitz condition.

Extends taming techniques to Milstein schemes for Le9vy SDEs.

Provides explicit schemes for super-linear drift coefficients.

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.