In this note we prove sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift. We study the approximation of jump-diffusion SDEs with non-adaptive as well as jump-adapted approximation schemes and provide lower error bounds of order $3/4$ for both classes of approximation schemes. This yields optimality of the transformation-based jump-adapted quasi-Milstein scheme.

翻译：本文证明了带有间断漂移的跳-扩散随机微分方程数值方法的锐利下界误差。我们研究了非自适应和跳适应两类逼近方案下跳-扩散随机微分方程的近似问题，并为这两类逼近方案提供了阶数为$3/4$的下界误差。这一结果证明了基于变换的跳适应拟Milstein方案的最优性。